Physical Review

Nonlocal Currents as Coordinates for Particles

Josip Z. Soln

Published Jul 25, 1968• 3 citations

Abstract

We investigate the possibility of formulating the dynamical theories in terms of nonlocal "currents." As an example, we formulate the nonrelativistic system of $n$ identical particles (with and without spin). From these models we learn that the extension to relativistic systems is possible. This is illustrated by treating the Thirring model in terms of nonlocal currents.

DOI: 10.1103/physrev.171.1773

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Physical Review

Nonlocal Currents as Coordinates for Particles

Josip Z. Soln

Published Jul 25, 1968• 3 citations

Publisher

Abstract

We investigate the possibility of formulating the dynamical theories in terms of nonlocal "currents." As an example, we formulate the nonrelativistic system of

n

identical particles (with and without spin). From these models we learn that the extension to relativistic systems is possible. This is illustrated by treating the Thirring model in terms of nonlocal currents.

DOI: 10.1103/physrev.171.1773

Related papers

Currents as Coordinates in Nonrelativistic Quantum Mechanics

WILLIAM J. PARDEE, Leonard Schlessinger, Jon Wright

Physical ReviewNov 25, 196811 citations

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David J. Gross

Physical ReviewJan 25, 19699 citations

Representations of Local Nonrelativistic Current Algebras

J. Grodnik, D. H. Sharp

In this paper we show how to specify the particle content of a nonrelativistic quantum theory of $N$ identical spinless particles in terms of observables like the particle number density and the flux density of particles. Our approach to this problem is through a study of the irreducible representations of the local, equal-time current algebra. It is shown how these representations define a functional representation of the current algebra, and that the Hamiltonian can be written in terms of the currents in a nonsingular fashion in any irreducible representation.In this paper we show how to specify the particle content of a nonrelativistic quantum theory of $N$ identical spinless particles in terms of observables like the particle number density and the flux density of particles. Our approach to this problem is through a study of the irreducible representations of the local, equal-time current algebra. It is shown how these representations define a functional representation of the current algebra, and that the Hamiltonian can be written in terms of the currents in a nonsingular fashion in any irreducible representation.

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Burke Ritchie

Abstract Electron or ion dynamics are treated using spin‐dependent quantum trajectories. These trajectories are inferred from the Dirac current, which contributes Schroedinger's current and additional spin‐dependent terms, all of which are of order c0 in the nonrelativistic regime of particle velocity, where c is the speed of light. The many‐body problem is treated precisely as in classical dynamics. Each electron or ion has its own equation of motion, which is the time‐dependent Dirac or the time‐dependent Schroedinger equation in the relativistic or nonrelativistic regime of particle velocity, respectively. As an example the theory is applied to the electronic structure of the helium atom, in which two electrons with opposite spin states are shown to correlate such that their quantum trajectories keep them on average on opposite sides of the nucleus. As the theory is time dependent, excited states are also generated. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011Abstract Electron or ion dynamics are treated using spin‐dependent quantum trajectories. These trajectories are inferred from the Dirac current, which contributes Schroedinger's current and additional spin‐dependent terms, all of which are of order c0 in the nonrelativistic regime of particle velocity, where c is the speed of light. The many‐body problem is treated precisely as in classical dynamics. Each electron or ion has its own equation of motion, which is the time‐dependent Dirac or the time‐dependent Schroedinger equation in the relativistic or nonrelativistic regime of particle velocity, respectively. As an example the theory is applied to the electronic structure of the helium atom, in which two electrons with opposite spin states are shown to correlate such that their quantum trajectories keep them on average on opposite sides of the nucleus. As the theory is time dependent, excited states are also generated. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

International Journal of Quantum ChemistryOct 13, 200910 citations

We investigate the possibility of formulating the dynamical theories in terms of nonlocal "currents." As an example, we formulate the nonrelativistic system of

n

In this paper we show how to specify the particle content of a nonrelativistic quantum theory of

N

identical spinless particles in terms of observables like the particle number density and the flux density of particles. Our approach to this problem is through a study of the irreducible representations of the local, equal-time current algebra. It is shown how these representations define a functional representation of the current algebra, and that the Hamiltonian can be written in terms of the currents in a nonsingular fashion in any irreducible representation.

{M}_{m}

, it possesses a covariant propagator, it leaves the space of positive-energy solutions of the Klein-Gordon equation invariant, and it gives rise to a covariant and conserved probability current on stochastic phase space. Furthermore, for states describing a particle moving at nonrelativistic speeds in relation to a given inertial frame, the relativistic propagation contracts into its nonrelativistic counterpart. The sharp-point limit $s\ensuremath{\rightarrow}+0$ of the relativistic

S

matrix also exists in each such inertial frame. The necessity of interactions acting at nonsharp configuration points for a consistent formulation of covariant relativistic one-particle dynamics is traced to the question of the nonexistence of covariant position operators in relativistic theories. The mandatory character of this feature is shown to be firmly rooted in the theory of quantum measurement.