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American Mathematical Society eBooks

Quantum field theory, statistical mechanics, and nonrelativistic quantum systems : a conference on spectral theory and mathematical physics in honor of Barry Simon's 60th birthday, March 27-31, 2006, California Institute of Technology, Pasadena, California

Fritz Gesztesy

Published Jan 1, 2007• 0 citations
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Abstract

Quantum field theory, statistical mechanics: Perspectives in statistical mechanics by M. Aizenman Coherent infrared representations in non-relativistic QED by T. Chen and J. Frohlich Quantum spin systems after DLS 1978 by B. Nachtergaele Barry Simon's contributions to quantum field theory by L. Rosen Nonrelativistic two-body and $N$-body quantum systems, resonances: Isoperimetric inequalities for eigenvalues of the Laplacian by M. S. Ashbaugh and R. D. Benguria Non-self-adjoint operators and pseudospectra by E. B. Davies Barry Simon's contribution to non-relativistic quantum mechanics: Two-body and $N$-body Schrodinger operators and resonances by R. Froese $N$-body quantum scattering and quantum resonances: An overview by C. Gerard Mathematical analysis of Born-Oppenheimer approximations by G. A. Hagedorn and A. Joye Perturbation theory and atomic resonances since Schrodinger's time by E. M. Harrell II On a theorem for quantum mechanical scattering theory by A. Lenard Analytic criteria in the qualitative spectral analysis of the Schrodinger operator by V. Maz'ya The spectral geometry of geometrically finite hyperbolic manifolds by P. Perry Topics in the theory of positive solutions of second-order elliptic and parabolic partial differential equations by Y. Pinchover Complex scaling in atomic physics: A staging ground for experimental mathematics and for extracting physics from otherwise impossible computations by W. P. Reinhardt Recent results on the Bethe-Sommerfeld conjecture by A. V. Sobolev Electric and magnetic fields, semiclassical limit: Recent developments in quantum mechanics with magnetic fields by L. Erdos Aspects of the integer quantum Hall effect by G. M. Graf Barry Simon's work on electric and magnetic fields and the semi-classical limit by I. W. Herbst Some bound state problems in quantum mechanics by D. Hundertmark.

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Mathematical results in quantum mechanics : a conference on QMATH-8, Mathematical Results in Quantum Mechanics Universidad Nacional Autónoma de México, Taxco, México, December 10-14, 2001

Ricardo Weder, Pavel Exner, Benoît Grébert

Blow-up for Schrodinger equation with pointwise nonlinearity by R. Adami Quantum electrodynamics of relativistic bound states with cutoffs. II by J.-M. Barbaroux, M. Dimassi, and J.-C. Guillot Scattering by a slab: An exact calculation by F. Bentosela and M. Tater Crystalline order in one dimensional Thomas-Fermi type models by X. Blanc and C. Le Bris New results on the spectrum of lattice Schrodinger operators and applications by J. Bourgain Reconstruction of the memory from partial boundary measurements by A. L. Bukhgeim, G. V. Dyatlov, and G. Uhlmann Asymptotics for nonlinear dissipative equations in the super critical case by R. E. Cardiel and P. I. Naumkin Edge states for quantum Hall Hamiltonians by J.-M. Combes, P. D. Hislop, and E. Soccorsi A semiclassical approach in linear response theory by M. Combescure and D. Robert Wigner-von Neumann-like potentials by J. Cruz-Sampedro Equilibrium potentials in scattering theory by M. Demuth and A. Noll Straight quantum waveguides with combined boundary conditions by J. Dittrich and J. Kriz Perturbation theory for the quantum time-evolution in rotating potentials by V. Enss, V. Kostrykin, and R. Schrader Two dimensional Pauli operator via scalar potential by L. Erdos and V. Vougalter A max-min principle for the ground state of the Dirac-Fock functional by M. J. Esteban and E. Sere On the regularity of the density of electronic wave functions by S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and T. O. Sorensen Enhanced binding through coupling to a photon field by C. Hainzl The large radius limit for coherent states on spheres by B. C. Hall and J. J. Mitchell Quantum scattering for potentials homogeneous of degree zero by I. Herbst and E. Skibsted Existence of the density of states for one-dimensional alloy-type potentials with small support by W. Kirsch and I. Veselic Statistical ensembles and density of states by V. Kostrykin and R. Schrader The Cauchy problem for the Toda lattice with a class of non-stabilized initial data by M. Kudryavtsev Absolutely continuous spectrum of Jacobi matrices by A. Laptev, S. Naboko, and O. Safronov Stability of matter in relativistic quantum electrodynamics by E. H. Lieb and M. Loss The algebra of observables in a magnetic field by M. Mantoiu and R. Purice Recent developments in value distribution theory for Schrodinger operators on the half line by D. B. Pearson Long time propagation results in quantum mechanics by D. Robert Comments on adiabatic quantum algorithms by M. B. Ruskai Tunneling destruction for a nonlinear Schrodinger equation by A. Sacchetti Symmetry breaking in a model of a rotating Bose gas by R. Seiringer Euler's constant in Segal-Bargmann analysis by S. B. Sontz Maxwell with a touch of Schrodinger by A. Tip Exponentially accurate semiclassical asymptotics by J. H. Toloza Some properties of the eigenvalues of a Schrodinger equation with energy-dependent potential by C. van der Mee and V. Pivovarchik The Bargmann transform for $L^2(S^3)$ and regularization of the Kepler problem by C. Villegas-Blas Schrodinger equations with superquadratic potentials by K. Yajima and G. Zhang Band spectrum of the Laplacian on a slab with the Dirichlet boundary condition on a grid by K. Yoshitomi Other talks Participants.

American Mathematical Society eBooks•Jan 1, 2002•0 citations

"Quantum Mechanics in Mathematics, Chemistry, and Physics"

Karl E. Gustafson, William P. Reinhardt

Total Cross Sections in Non-Relativistic Scattering Theory.- Classical-Quantum Correspondence in Non-Linear Systems.- Real Axis Asymptotics and Estimates of Hamiltonian Resolvent Kernels.- Statistical Inference in Quantum Mechanics.- Schrodinger Operators with Oscillating Potentials.- Time Delay and Resonance in Simple Scattering.- A Study of the Helmholtz Operator.- Invariant Manifolds and Bifurcations in the Taylor Problem.- On the Dimension of a Finite Difference Approximation to Divergence-Free Vectors.- Intramolecular Dynamics in the Quasiperiodic and Stochastic Regimes.- Problems in the Semiclassical Quantization of Integrable and Nonintegrable Classical Dynamical Systems.- Nonselfadjoint Operators in Diffraction and Scattering.- One-Dimensional Crystals in an External Field.- Dynamics of Forced Coupled Oscillators: Classical Phenomenology of Infrared Multiphoton Absorption.- Irreversibility and Stochasticity of Chemical Processes.- On the Representations of the Local Current Algebra and the Group of Diffeomorphisms (I).- Regular and Chaotic Regimes in Quantum Mechanics.- Barrier Penetration and Exponential Decay in the Stark Effect.- A Nonlinear Schrodinger Equation Yielding the Shape of Molecules by Spontaneous Symmetry Breaking.- Classical Limit of the Number of Quantum States.- Formal Integrals for a Nonintegrable Dynamical System: Preliminary Report.- On a Generalized Weyl-Von Neumann Converse Theorem.- Scattering Theory in Many-Body Quantum Systems. Analyticity of the Scattered Matrix.- Existence, Uniqueness, Stability and Calculation of the Stationary Regimes in Some Nonlinear Systems.- Weighted Trigonometric Approximations in L2(Rn).- The Phenomenon of Magnetic Pairing and Exactly Soluble Models of Magnetic Resonances.- Dyons Solutions to Yang-Mills Equations.- Asymptotic Resonance Properties of the Finite-Dimensional Friedrichs Model.- Self-Consistent Field Methods for Metastable Electronic States: A Promising Extension of the Complex Coordinate Technique.- Timestep Control for the Numerical Solutions of Initial-Boundary-Value Problems.- Quantum Mechanical Angular Distributions and Group Representations on Banach Spaces.- Tensor Product Decomposition of Holomorphically Induced Representations and Clebsch-Gordan Coefficients.- Orthogonal Laurent Polynomials and Gaussian Quadrature.- Measurement Theory with Instruments Treated Partially Quantum Mechanically.- Transition Maps and Locality.- The Feynman-Kac Formula for Boson Wiener Processes.- On Nonunitary Equivalence Between Unitary Group of Dynamics and Contraction Semigroups of Markov Processes.

•Nov 1, 2011•50 citations

Studies in Mathematical Physics: Essays in Honor of Valentine Bargmann

Some of the articles in this collection give up-to-date accounts of areas in mathematical physics to which Valentine Bargmann made pioneering contributions. The others treat a selection of the most interesting current topics in the field. The contributions include both reviews and original results. Contents: The Inverse r-Squared Force (Henry D. I. Abarbanel; Certain Hilbert Spaces of Analytic Functions Associated with the Heisenberg Group (Donald Babbitt); Lower Bound for the Ground State Energy of the Schrodinger Equation Using the Sharp Form of Young's Inequality (John F. Barnes, Herm Jan Brascamp, and Elliott II. Lieb); Alternative Theories of Gravitation (Peter G. Bergmann; )Generalized Wronskian Relations (F. Calogero); Old and New Approaches to the Inverse-Scattering Problem (Freeman J. Dyson); A Family of Optimal Conditions for the Absence of Bound States in a Potential (V. Glaser, A. Martin, H. Grosse, and W. Thirring); Spinning Tops in External Fields (Sergio Hojman and Tullio Regge); Measures on the Finite Dimensional Subspaces of a Hilbert Space (Res Jost); The Froissart Bound and Crossing Symmetry (N. N. Khuri); Intertwining Operators for SL(n,R) (A. W. Knapp and E. M. Stein); Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relations to Sobolev Inequalities (Elliott H. Lieb and Walter Thirriny); On the Number of Bound States of Two Body Schrodinger Operators (Barry Simon); Quantum Dynamics: From Automorphism to Hamiltonian (Barry Simon); Semiclassical Analysis Illuminates the Connection between Potential and Bound States and Scattering (John Archibald Wheeler); Instability Phenomena in the External Field Problem for Two Classes of Relativistic Wave Equations (A. S. Wightman) Originally published in 1976. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Princeton University Press eBooks•Apr 24, 2015•166 citations

Ideas and methods in quantum and statistical physics

Sergio A Albeverio, Helge Holden, Jens Erik Fenstad +1 more

Preface Part I. Quantum Mechanics: 1. On the low density of Boson models: Langevin equation L. Accardi and L. Y. Gang 2. Schrodinger operators with potentials supported by null sets S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, W. Karwowski and T. Lindstrom 3. Landau Hamiltonians on symmetric spaces J. E. Avron and A. Pnueli 4. Renormalization group analysis and quasicrystals J. Bellissard 5. The measurement problem in the stochastic formulation of quantum mechanics Ph. Blanchard, M. Cini and M. Serva 6. Schrodinger operators at threshold D. Bolle 7. Spectral analysis and scattering theory for Schrodinger operators with an interaction supported by a regular curve J. F. Brasche and A. Teta 8. Lattice models of solids V. V. Evstratov and B. S. Pavlov 9. Schrodinger operators on unusual manifolds P. Exner and P. Seba 10. High energy resolvent estimates for Schrodinger operators A. Jensen 11. Point interactions as solvable models W. Kirsch 12. Stochastic model of quantum mechanics V. P. Maslov Part II. Quantum Field Theory: 13. Maximality of infinite dimensional Dirichlet forms and Hoegh-Krohn's model of quantum fields S. Albeverio and S. Kusuoka 14. Global Markov property in quantum field theory and statistical mechanics: a review on results and problems S. Albeverio and B. Zegarlinski 15. Hypercontractivity: a bibliographic review E. B. Davies, L. B. Gross and B. Simon 16. Progress and problems in algebraic quantum field theory S. Doplicher 17. Hoegh-Krohn's model of quantum fields and the absolute continuity of measures S. Kusuoka 18. Baryon states in lattice QCD R. A. Minlos and E. A. Zhinzhina 19. The energy of a Weyl soliton R. F. Streater Part III. Statistical Physics: 20. Morphology and classification of galaxies: a stochastic model S. Albeverio, Ph. Blanchard, D. Gandolfo, R. Hoegh-Krohn and M. Mebkhout 21. Thermodynamic inequalities for the surface tension and the geometry of the Wulff construction R. L. Dobrushin and S. B. Shlosman 22. Verification of the global Markov property for strongly coupled trigonometric interactions R. Gielerak 23. Decomposition of Ising models and the Mayer expansion C. M. Newman and G. A. Baker, Jr 24. Towards time-dynamics for bosonic systems in quantum statistical mechanics A. G. Shuhov, Yu. M. Suhov and A. V. Teslenko 25. Towards time-dynamics for bosonic systems in quantum statistical mechanics, 2 A. G. Shuhov and Yu. M. Suhov.

Cambridge University Press eBooks•Jun 1, 1992•52 citations

Quantum Field Theory and Statistical Mechanics: Expositions

James G. Glimm, Arthur M. Jaffe

I Infinite Renormalization of the Hamiltonian Is Necessary.- II Quantum Field Theory Models.- I. The ?22n Model.- Fock space.- Q space.- The Hamiltonian H(g).- Removing the space cutoff.- Lorentz covariance and the Haag-Kastler axioms.- II. The Yukawa Model.- Preliminaries.- First and second order estimates.- Resolvent convergence and self adjointness.- The Heisenberg picture.- III Boson Quantum Field Models.- I. General Results.- Hermite operators.- Gaussian measures and the Schrodinger representation.- Hermite expansions and Fock space.- II. The Solution of Two-Dimensional Boson Models.- The interaction Hamiltonian.- The free Hamiltonian.- Self-adjointness of H(g).- The local algebras and the Lorentz group automorphisms.- IV Boson Quantum Field Models.- III. Further Developments.- Locally normal representations of the observables.- The construction of the physical vaccum.- Formal perturbation theory and models in three space-time dimensions.- V The Particle Structure of the Weakly Coupled P(?)2 Model and Other Applications of High Temperature Expansions.- I. Physics of Quantum Field Models.- Five years of models.- From estimates to physics.- Bound states and resonances.- Phase space localization and renormalization.- VI The Particle Structure of the Weakly Coupled P(?)2 Model and Other Applications of High Temperature Expansions.- II. The Cluster Expansion.- The main results.- The cluster expansion.- Clustering and analyticity: proof of the main results.- Convergence: the main ideas.- An equation of Kirkwood-Salsburg type.- Covariance operators.- Derivatives of covariance operators.- Gaussian integrals.- Convergence: the proof completed.- VII Particles and Bound States and Progess Toward Unitarity and Scaling.- VIII Critical Problems in Quantum Fields.- IX Existence of Phase Transitions for ?24 Quantum Fields.- X Critical Exponents and Renormalization in the ?4 Scaling Limit.- Formulation of the problem.- The scaling and critical point limits.- Renormalization of the ?2(x) field.- Existence of the scaling limit.- The Josephson inequality.- XI A Tutorial Course in Constructive Field Theory.- e?tH as a functional integral.- Examples.- Applications of the functional integral representation.- Ising, Gaussian and scaling limits.- Main results.- Correlation inequalities.- Absence of even bound states.- Bound on g.- Bound on dm2/d? and particles.- The conjecture ?(6) ? 0.- Cluster expansions.- The region of convergence.- The zeroth order expansion.- The primitive expansion.- Factorization and partial resummation.- Typical applications.

•Jan 1, 1985•5 citations

Adventures in mathematical physics : International Conference in honor of Jean-Michel Combes on Transport and Spectral Problems in Quantum Mechanics, September 4-6, 2006, Université de Cergy-Pontoise, Cergy-Pontoise, France

François Germinet, Peter D. Hislop

On the emptiness formation probability in quasi-free states by W. H. Aschbacher Wegner-Stollmann type estimates for some quantum lattice systems by V. Chulaevsky The mutually unbiased bases revisited by M. Combescure Pertubative vs. variational methods in the study of carbon nanotubes by H. D. Cornean, T. G. Pedersen, and B. Ricaud Normal transport at positive temperatures in classical Hamiltonian open systems by S. De Bievre, P. Lafitte, and P. E. Parris Equivalence of resolvent and scattering resonances on quantum graphs by P. Exner and J. Lipovsky Optimal uniform elliptic estimates for the Ginzburg-Landau system by S. Fournais and B. Helffer Localization for a continuum Cantor-Anderson Hamiltonian by F. Germinet and A. Klein Generalized fractal dimensions on the negative axis for non compactly supported measures by F. Germinet and S. Tcheremchantsev Localization for Schrodinger operators with random vector potentials by F. Ghribi, P. D. Hislop, and F. Klopp Vibrational levels associated with hydrogen bonds and semiclassical Hamiltonian normal forms by G. A. Hagedorn and A. Joye On the strict positivity of entropy production by V. Jaksic and C.-A. Pillet Uniqueness results for transient dynamics of quantum systems by A. Jensen and G. Nenciu Heat kernels on metric graphs and a trace formula by V. Kostrykin, J. Potthoff, and R. Schrader On a random matrix model of quantum relaxation by J. L. Lebowitz, A. Lytova, and L. Pastur Revivals of wave packets and Bohr-Sommerfeld quantization rules by D. Robert On a linear stochastic wave equation modeling heat flow by L. E. Thomas and Y. Wang Exponential decay of eigenfunctions of first order systems by D. R. Yafaev.

American Mathematical Society eBooks•Jan 1, 2007•0 citations
Quantum field theory, statistical mechanics: Perspectives in statistical mechanics by M. Aizenman Coherent infrared representations in non-relativistic QED by T. Chen and J. Frohlich Quantum spin systems after DLS 1978 by B. Nachtergaele Barry Simon's contributions to quantum field theory by L. Rosen Nonrelativistic two-body and NNN-body quantum systems, resonances: Isoperimetric inequalities for eigenvalues of the Laplacian by M. S. Ashbaugh and R. D. Benguria Non-self-adjoint operators and pseudospectra by E. B. Davies Barry Simon's contribution to non-relativistic quantum mechanics: Two-body and NNN-body Schrodinger operators and resonances by R. Froese NNN-body quantum scattering and quantum resonances: An overview by C. Gerard Mathematical analysis of Born-Oppenheimer approximations by G. A. Hagedorn and A. Joye Perturbation theory and atomic resonances since Schrodinger's time by E. M. Harrell II On a theorem for quantum mechanical scattering theory by A. Lenard Analytic criteria in the qualitative spectral analysis of the Schrodinger operator by V. Maz'ya The spectral geometry of geometrically finite hyperbolic manifolds by P. Perry Topics in the theory of positive solutions of second-order elliptic and parabolic partial differential equations by Y. Pinchover Complex scaling in atomic physics: A staging ground for experimental mathematics and for extracting physics from otherwise impossible computations by W. P. Reinhardt Recent results on the Bethe-Sommerfeld conjecture by A. V. Sobolev Electric and magnetic fields, semiclassical limit: Recent developments in quantum mechanics with magnetic fields by L. Erdos Aspects of the integer quantum Hall effect by G. M. Graf Barry Simon's work on electric and magnetic fields and the semi-classical limit by I. W. Herbst Some bound state problems in quantum mechanics by D. Hundertmark.
Blow-up for Schrodinger equation with pointwise nonlinearity by R. Adami Quantum electrodynamics of relativistic bound states with cutoffs. II by J.-M. Barbaroux, M. Dimassi, and J.-C. Guillot Scattering by a slab: An exact calculation by F. Bentosela and M. Tater Crystalline order in one dimensional Thomas-Fermi type models by X. Blanc and C. Le Bris New results on the spectrum of lattice Schrodinger operators and applications by J. Bourgain Reconstruction of the memory from partial boundary measurements by A. L. Bukhgeim, G. V. Dyatlov, and G. Uhlmann Asymptotics for nonlinear dissipative equations in the super critical case by R. E. Cardiel and P. I. Naumkin Edge states for quantum Hall Hamiltonians by J.-M. Combes, P. D. Hislop, and E. Soccorsi A semiclassical approach in linear response theory by M. Combescure and D. Robert Wigner-von Neumann-like potentials by J. Cruz-Sampedro Equilibrium potentials in scattering theory by M. Demuth and A. Noll Straight quantum waveguides with combined boundary conditions by J. Dittrich and J. Kriz Perturbation theory for the quantum time-evolution in rotating potentials by V. Enss, V. Kostrykin, and R. Schrader Two dimensional Pauli operator via scalar potential by L. Erdos and V. Vougalter A max-min principle for the ground state of the Dirac-Fock functional by M. J. Esteban and E. Sere On the regularity of the density of electronic wave functions by S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and T. O. Sorensen Enhanced binding through coupling to a photon field by C. Hainzl The large radius limit for coherent states on spheres by B. C. Hall and J. J. Mitchell Quantum scattering for potentials homogeneous of degree zero by I. Herbst and E. Skibsted Existence of the density of states for one-dimensional alloy-type potentials with small support by W. Kirsch and I. Veselic Statistical ensembles and density of states by V. Kostrykin and R. Schrader The Cauchy problem for the Toda lattice with a class of non-stabilized initial data by M. Kudryavtsev Absolutely continuous spectrum of Jacobi matrices by A. Laptev, S. Naboko, and O. Safronov Stability of matter in relativistic quantum electrodynamics by E. H. Lieb and M. Loss The algebra of observables in a magnetic field by M. Mantoiu and R. Purice Recent developments in value distribution theory for Schrodinger operators on the half line by D. B. Pearson Long time propagation results in quantum mechanics by D. Robert Comments on adiabatic quantum algorithms by M. B. Ruskai Tunneling destruction for a nonlinear Schrodinger equation by A. Sacchetti Symmetry breaking in a model of a rotating Bose gas by R. Seiringer Euler's constant in Segal-Bargmann analysis by S. B. Sontz Maxwell with a touch of Schrodinger by A. Tip Exponentially accurate semiclassical asymptotics by J. H. Toloza Some properties of the eigenvalues of a Schrodinger equation with energy-dependent potential by C. van der Mee and V. Pivovarchik The Bargmann transform for L2(S3)L^2(S^3)L2(S3) and regularization of the Kepler problem by C. Villegas-Blas Schrodinger equations with superquadratic potentials by K. Yajima and G. Zhang Band spectrum of the Laplacian on a slab with the Dirichlet boundary condition on a grid by K. Yoshitomi Other talks Participants.
Total Cross Sections in Non-Relativistic Scattering Theory.- Classical-Quantum Correspondence in Non-Linear Systems.- Real Axis Asymptotics and Estimates of Hamiltonian Resolvent Kernels.- Statistical Inference in Quantum Mechanics.- Schrodinger Operators with Oscillating Potentials.- Time Delay and Resonance in Simple Scattering.- A Study of the Helmholtz Operator.- Invariant Manifolds and Bifurcations in the Taylor Problem.- On the Dimension of a Finite Difference Approximation to Divergence-Free Vectors.- Intramolecular Dynamics in the Quasiperiodic and Stochastic Regimes.- Problems in the Semiclassical Quantization of Integrable and Nonintegrable Classical Dynamical Systems.- Nonselfadjoint Operators in Diffraction and Scattering.- One-Dimensional Crystals in an External Field.- Dynamics of Forced Coupled Oscillators: Classical Phenomenology of Infrared Multiphoton Absorption.- Irreversibility and Stochasticity of Chemical Processes.- On the Representations of the Local Current Algebra and the Group of Diffeomorphisms (I).- Regular and Chaotic Regimes in Quantum Mechanics.- Barrier Penetration and Exponential Decay in the Stark Effect.- A Nonlinear Schrodinger Equation Yielding the Shape of Molecules by Spontaneous Symmetry Breaking.- Classical Limit of the Number of Quantum States.- Formal Integrals for a Nonintegrable Dynamical System: Preliminary Report.- On a Generalized Weyl-Von Neumann Converse Theorem.- Scattering Theory in Many-Body Quantum Systems. Analyticity of the Scattered Matrix.- Existence, Uniqueness, Stability and Calculation of the Stationary Regimes in Some Nonlinear Systems.- Weighted Trigonometric Approximations in L2(Rn).- The Phenomenon of Magnetic Pairing and Exactly Soluble Models of Magnetic Resonances.- Dyons Solutions to Yang-Mills Equations.- Asymptotic Resonance Properties of the Finite-Dimensional Friedrichs Model.- Self-Consistent Field Methods for Metastable Electronic States: A Promising Extension of the Complex Coordinate Technique.- Timestep Control for the Numerical Solutions of Initial-Boundary-Value Problems.- Quantum Mechanical Angular Distributions and Group Representations on Banach Spaces.- Tensor Product Decomposition of Holomorphically Induced Representations and Clebsch-Gordan Coefficients.- Orthogonal Laurent Polynomials and Gaussian Quadrature.- Measurement Theory with Instruments Treated Partially Quantum Mechanically.- Transition Maps and Locality.- The Feynman-Kac Formula for Boson Wiener Processes.- On Nonunitary Equivalence Between Unitary Group of Dynamics and Contraction Semigroups of Markov Processes.
Some of the articles in this collection give up-to-date accounts of areas in mathematical physics to which Valentine Bargmann made pioneering contributions. The others treat a selection of the most interesting current topics in the field. The contributions include both reviews and original results. Contents: The Inverse r-Squared Force (Henry D. I. Abarbanel; Certain Hilbert Spaces of Analytic Functions Associated with the Heisenberg Group (Donald Babbitt); Lower Bound for the Ground State Energy of the Schrodinger Equation Using the Sharp Form of Young's Inequality (John F. Barnes, Herm Jan Brascamp, and Elliott II. Lieb); Alternative Theories of Gravitation (Peter G. Bergmann; )Generalized Wronskian Relations (F. Calogero); Old and New Approaches to the Inverse-Scattering Problem (Freeman J. Dyson); A Family of Optimal Conditions for the Absence of Bound States in a Potential (V. Glaser, A. Martin, H. Grosse, and W. Thirring); Spinning Tops in External Fields (Sergio Hojman and Tullio Regge); Measures on the Finite Dimensional Subspaces of a Hilbert Space (Res Jost); The Froissart Bound and Crossing Symmetry (N. N. Khuri); Intertwining Operators for SL(n,R) (A. W. Knapp and E. M. Stein); Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relations to Sobolev Inequalities (Elliott H. Lieb and Walter Thirriny); On the Number of Bound States of Two Body Schrodinger Operators (Barry Simon); Quantum Dynamics: From Automorphism to Hamiltonian (Barry Simon); Semiclassical Analysis Illuminates the Connection between Potential and Bound States and Scattering (John Archibald Wheeler); Instability Phenomena in the External Field Problem for Two Classes of Relativistic Wave Equations (A. S. Wightman) Originally published in 1976. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Preface Part I. Quantum Mechanics: 1. On the low density of Boson models: Langevin equation L. Accardi and L. Y. Gang 2. Schrodinger operators with potentials supported by null sets S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, W. Karwowski and T. Lindstrom 3. Landau Hamiltonians on symmetric spaces J. E. Avron and A. Pnueli 4. Renormalization group analysis and quasicrystals J. Bellissard 5. The measurement problem in the stochastic formulation of quantum mechanics Ph. Blanchard, M. Cini and M. Serva 6. Schrodinger operators at threshold D. Bolle 7. Spectral analysis and scattering theory for Schrodinger operators with an interaction supported by a regular curve J. F. Brasche and A. Teta 8. Lattice models of solids V. V. Evstratov and B. S. Pavlov 9. Schrodinger operators on unusual manifolds P. Exner and P. Seba 10. High energy resolvent estimates for Schrodinger operators A. Jensen 11. Point interactions as solvable models W. Kirsch 12. Stochastic model of quantum mechanics V. P. Maslov Part II. Quantum Field Theory: 13. Maximality of infinite dimensional Dirichlet forms and Hoegh-Krohn's model of quantum fields S. Albeverio and S. Kusuoka 14. Global Markov property in quantum field theory and statistical mechanics: a review on results and problems S. Albeverio and B. Zegarlinski 15. Hypercontractivity: a bibliographic review E. B. Davies, L. B. Gross and B. Simon 16. Progress and problems in algebraic quantum field theory S. Doplicher 17. Hoegh-Krohn's model of quantum fields and the absolute continuity of measures S. Kusuoka 18. Baryon states in lattice QCD R. A. Minlos and E. A. Zhinzhina 19. The energy of a Weyl soliton R. F. Streater Part III. Statistical Physics: 20. Morphology and classification of galaxies: a stochastic model S. Albeverio, Ph. Blanchard, D. Gandolfo, R. Hoegh-Krohn and M. Mebkhout 21. Thermodynamic inequalities for the surface tension and the geometry of the Wulff construction R. L. Dobrushin and S. B. Shlosman 22. Verification of the global Markov property for strongly coupled trigonometric interactions R. Gielerak 23. Decomposition of Ising models and the Mayer expansion C. M. Newman and G. A. Baker, Jr 24. Towards time-dynamics for bosonic systems in quantum statistical mechanics A. G. Shuhov, Yu. M. Suhov and A. V. Teslenko 25. Towards time-dynamics for bosonic systems in quantum statistical mechanics, 2 A. G. Shuhov and Yu. M. Suhov.
I Infinite Renormalization of the Hamiltonian Is Necessary.- II Quantum Field Theory Models.- I. The ?22n Model.- Fock space.- Q space.- The Hamiltonian H(g).- Removing the space cutoff.- Lorentz covariance and the Haag-Kastler axioms.- II. The Yukawa Model.- Preliminaries.- First and second order estimates.- Resolvent convergence and self adjointness.- The Heisenberg picture.- III Boson Quantum Field Models.- I. General Results.- Hermite operators.- Gaussian measures and the Schrodinger representation.- Hermite expansions and Fock space.- II. The Solution of Two-Dimensional Boson Models.- The interaction Hamiltonian.- The free Hamiltonian.- Self-adjointness of H(g).- The local algebras and the Lorentz group automorphisms.- IV Boson Quantum Field Models.- III. Further Developments.- Locally normal representations of the observables.- The construction of the physical vaccum.- Formal perturbation theory and models in three space-time dimensions.- V The Particle Structure of the Weakly Coupled P(?)2 Model and Other Applications of High Temperature Expansions.- I. Physics of Quantum Field Models.- Five years of models.- From estimates to physics.- Bound states and resonances.- Phase space localization and renormalization.- VI The Particle Structure of the Weakly Coupled P(?)2 Model and Other Applications of High Temperature Expansions.- II. The Cluster Expansion.- The main results.- The cluster expansion.- Clustering and analyticity: proof of the main results.- Convergence: the main ideas.- An equation of Kirkwood-Salsburg type.- Covariance operators.- Derivatives of covariance operators.- Gaussian integrals.- Convergence: the proof completed.- VII Particles and Bound States and Progess Toward Unitarity and Scaling.- VIII Critical Problems in Quantum Fields.- IX Existence of Phase Transitions for ?24 Quantum Fields.- X Critical Exponents and Renormalization in the ?4 Scaling Limit.- Formulation of the problem.- The scaling and critical point limits.- Renormalization of the ?2(x) field.- Existence of the scaling limit.- The Josephson inequality.- XI A Tutorial Course in Constructive Field Theory.- e?tH as a functional integral.- Examples.- Applications of the functional integral representation.- Ising, Gaussian and scaling limits.- Main results.- Correlation inequalities.- Absence of even bound states.- Bound on g.- Bound on dm2/d? and particles.- The conjecture ?(6) ? 0.- Cluster expansions.- The region of convergence.- The zeroth order expansion.- The primitive expansion.- Factorization and partial resummation.- Typical applications.
On the emptiness formation probability in quasi-free states by W. H. Aschbacher Wegner-Stollmann type estimates for some quantum lattice systems by V. Chulaevsky The mutually unbiased bases revisited by M. Combescure Pertubative vs. variational methods in the study of carbon nanotubes by H. D. Cornean, T. G. Pedersen, and B. Ricaud Normal transport at positive temperatures in classical Hamiltonian open systems by S. De Bievre, P. Lafitte, and P. E. Parris Equivalence of resolvent and scattering resonances on quantum graphs by P. Exner and J. Lipovsky Optimal uniform elliptic estimates for the Ginzburg-Landau system by S. Fournais and B. Helffer Localization for a continuum Cantor-Anderson Hamiltonian by F. Germinet and A. Klein Generalized fractal dimensions on the negative axis for non compactly supported measures by F. Germinet and S. Tcheremchantsev Localization for Schrodinger operators with random vector potentials by F. Ghribi, P. D. Hislop, and F. Klopp Vibrational levels associated with hydrogen bonds and semiclassical Hamiltonian normal forms by G. A. Hagedorn and A. Joye On the strict positivity of entropy production by V. Jaksic and C.-A. Pillet Uniqueness results for transient dynamics of quantum systems by A. Jensen and G. Nenciu Heat kernels on metric graphs and a trace formula by V. Kostrykin, J. Potthoff, and R. Schrader On a random matrix model of quantum relaxation by J. L. Lebowitz, A. Lytova, and L. Pastur Revivals of wave packets and Bohr-Sommerfeld quantization rules by D. Robert On a linear stochastic wave equation modeling heat flow by L. E. Thomas and Y. Wang Exponential decay of eigenfunctions of first order systems by D. R. Yafaev.