Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/9810043

Coherent State Path Integrals at (Nearly) 40

John R. Klauder

Published Oct 14, 1998• 4 citations
arXivHTMLPDF

Abstract

Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time regularization that may involve a Wiener measure concentrated on continuous phase space paths. The introduction of constraints is both natural and economical in coherent state path integrals involving only the dynamical and Lagrange multiplier variables. A preliminary indication of how these procedures may possibly be applied to quantum gravity is briefly discussed.

DOI
10.48550/arxiv.quant-ph/9810043

Related papers

Selecta from a Life-Long Obsession with Path Integrals

John R. Klauder, Christopher Casenas Bernido, M. Victoria Carpio-Bernido

The definition and interpretation of canonical, phase space path integrals has evolved over many years to achieve a form that now admits a correct and rigorous formulation, which is also covariant under canonical coordinate transformations. Such formulations involve coherent state representations, which, in their modern version, were originally introduced as an alternative tool to construct phase space path integrals. Moreover, coherent state representations lead to physical interpretations that are more natural than those afforded by more traditional representations. Suitable continuous time regularization procedures lead to a covariant phase space path integral formulation that greatly clarifies the vague phrase that canonical quantization requires Cartesian coordinates.

AIP conference proceedings•Jan 1, 2008•0 citations

Weak Coherent States and their Path Integrals

Lorenz Hartmann

Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise e.g. in the case that a group acts on an inadmissible fiducial vector. Motivated by the recent Affine Quantum Gravity Program, the present work studies the path integral representation of the affine weak coherent state matrix elements of the unitary time-evolution operator. Since weak coherent states do not admit a resolution of unity, it is clear that the standard way of constructing a path integral, by time slicing, is predestined to fail. Instead, a well-defined path integral with Wiener measure, based on a continuous-time regularization, is used to approach this problem. The dynamics is rigorously established for linear Hamiltonians, and the difficulties presented by more general Hamiltonians are addressed.

arXiv:hep-th/0308185•Aug 27, 2003•2 citations

Continuous-Time Regularized Path Integrals

John R. Klauder

Up to this point we have focused on temporal lattice regularizations in order to give meaning to the traditional configuration and phase space path integrals including coherent state phase space path integrals. In this chapter, we take up the question of introducing a continuous-time regularization procedure into a formal phase space path integral. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Birkhäuser Boston eBooks•Oct 28, 2010•1 citation

Weak coherent state path integrals

Lorenz Hartmann, John R. Klauder

Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise, e.g., in the case that a group acts on an inadmissible fiducial vector. Motivated by the recent Affine Quantum Gravity Program, the present article studies the path integral representation of the affine weak coherent state matrix elements of the unitary time-evolution operator. Since weak coherent states do not admit a resolution of unity, it is clear that the standard way of constructing a path integral, by time slicing, is predestined to fail. Instead a well-defined path integral with Wiener measure, based on a continuous-time regularization, is used to approach this problem. The dynamics is rigorously established for linear Hamiltonians, and the difficulties presented by more general Hamiltonians are addressed.

arXiv:hep-th/0309184•Journal of Mathematical Physics•Dec 19, 2003•6 citations

Weak Coherent State Path Integrals

Lorenz Hartmann, John R. Klauder

Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise e.g. in the case that a group acts on an inadmissible fiducial vector. Motivated by the recent Affine Quantum Gravity Program, the present article studies the path integral representation of the affine weak coherent state matrix elements of the unitary time-evolution operator. Since weak coherent states do not admit a resolution of unity, it is clear that the standard way of constructing a path integral, by time slicing, is predestined to fail. Instead a well-defined path integral with Wiener measure, based on a continuous-time regularization, is used to approach this problem. The dynamics is rigorously established for linear Hamiltonians, and the difficulties presented by more general Hamiltonians are addressed. I.

•Jan 1, 2003•4 citations

Wiener and Poisson process regularization for coherent-state path integrals

Robert Alicki, John R. Klauder

By introducing a suitable continuous-time regularization into a formal phase-space path integral it follows that the propagator is given by the limit of well-defined functional integrals involving standard stochastic processes and their associated probability measures. Such regularizations require pinning of both coordinate and momenta variables, and automatically lead to coherent-state representations. It is found that each standard independent increment process, involving a superposition of a Wiener and a Poisson process, is associated with a specific, generally non-Gaussian, fiducial vector with which the coherent states are defined.

Journal of Mathematical Physics•Sep 1, 1993•4 citations
Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time regularization that may involve a Wiener measure concentrated on continuous phase space paths. The introduction of constraints is both natural and economical in coherent state path integrals involving only the dynamical and Lagrange multiplier variables. A preliminary indication of how these procedures may possibly be applied to quantum gravity is briefly discussed.
The definition and interpretation of canonical, phase space path integrals has evolved over many years to achieve a form that now admits a correct and rigorous formulation, which is also covariant under canonical coordinate transformations. Such formulations involve coherent state representations, which, in their modern version, were originally introduced as an alternative tool to construct phase space path integrals. Moreover, coherent state representations lead to physical interpretations that are more natural than those afforded by more traditional representations. Suitable continuous time regularization procedures lead to a covariant phase space path integral formulation that greatly clarifies the vague phrase that canonical quantization requires Cartesian coordinates.
Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise e.g. in the case that a group acts on an inadmissible fiducial vector. Motivated by the recent Affine Quantum Gravity Program, the present work studies the path integral representation of the affine weak coherent state matrix elements of the unitary time-evolution operator. Since weak coherent states do not admit a resolution of unity, it is clear that the standard way of constructing a path integral, by time slicing, is predestined to fail. Instead, a well-defined path integral with Wiener measure, based on a continuous-time regularization, is used to approach this problem. The dynamics is rigorously established for linear Hamiltonians, and the difficulties presented by more general Hamiltonians are addressed.
Up to this point we have focused on temporal lattice regularizations in order to give meaning to the traditional configuration and phase space path integrals including coherent state phase space path integrals. In this chapter, we take up the question of introducing a continuous-time regularization procedure into a formal phase space path integral. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise, e.g., in the case that a group acts on an inadmissible fiducial vector. Motivated by the recent Affine Quantum Gravity Program, the present article studies the path integral representation of the affine weak coherent state matrix elements of the unitary time-evolution operator. Since weak coherent states do not admit a resolution of unity, it is clear that the standard way of constructing a path integral, by time slicing, is predestined to fail. Instead a well-defined path integral with Wiener measure, based on a continuous-time regularization, is used to approach this problem. The dynamics is rigorously established for linear Hamiltonians, and the difficulties presented by more general Hamiltonians are addressed.
Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise e.g. in the case that a group acts on an inadmissible fiducial vector. Motivated by the recent Affine Quantum Gravity Program, the present article studies the path integral representation of the affine weak coherent state matrix elements of the unitary time-evolution operator. Since weak coherent states do not admit a resolution of unity, it is clear that the standard way of constructing a path integral, by time slicing, is predestined to fail. Instead a well-defined path integral with Wiener measure, based on a continuous-time regularization, is used to approach this problem. The dynamics is rigorously established for linear Hamiltonians, and the difficulties presented by more general Hamiltonians are addressed. I.
By introducing a suitable continuous-time regularization into a formal phase-space path integral it follows that the propagator is given by the limit of well-defined functional integrals involving standard stochastic processes and their associated probability measures. Such regularizations require pinning of both coordinate and momenta variables, and automatically lead to coherent-state representations. It is found that each standard independent increment process, involving a superposition of a Wiener and a Poisson process, is associated with a specific, generally non-Gaussian, fiducial vector with which the coherent states are defined.