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Progress of Theoretical Physics

Description of Mixed States Based on the Time-Dependent Hartree-Fock Theory. I: Formalism of Thermo Field Dynamics in Canonical Theory with Constraints

A. Kuriyama, João da Providência, M. Yamamura

Published Sep 1, 1990• 2 citations
Publisher

Abstract

Formalism of thermo field dynamics in classical mechanics with constraints, which is a natural consequence of the time-dependent Hartree-Fock theory for mixed states, is reformulated under the introduction of a gauge fixing condition. With the aid of this condition, the formulation is performed in the frame of Dirac's canonical theory with constraints. Any physical quantity can be expressed in terms of constraint-independent canonical variables.

DOI
10.1143/ptp/84.3.452

Related papers

Description of Mixed States Based on the Time-Dependent Hartree-Fock Theory. I

A. Kuriyama, João da Providência, Masatoshi Yamamura

Formalism of thermo field dynamics in classical mechanics with constraints, which is a natural consequence of the time-dependent Hartree-Fock theory for mixed states, is reformulated under the introduction of a gauge fixing condition. With the aid of this condition, the formulation is performed in the frame of Dirac's canonical theory with constraints. Any physical quantity can be expressed in terms of constraint-independent canonical variables.

Progress of Theoretical Physics•Sep 1, 1990•0 citations

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Description of Mixed States Based on the Time-Dependent Hartree-Fock Theory. II: Classical Boson Expansion

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As a continuation of Part I, a concrete procedure for solving the basic equations derived in I is presented. The cases of zeroth, first and second order approximation for the solution of the basic equations are discussed. The results are shown in terms of the power series expansion for the constraint-independent canonical variables, i.e., classical boson expansion. Finally, Hamilton's equation of motion is derived.

Progress of Theoretical Physics•Dec 1, 1990•1 citation
Formalism of thermo field dynamics in classical mechanics with constraints, which is a natural consequence of the time-dependent Hartree-Fock theory for mixed states, is reformulated under the introduction of a gauge fixing condition. With the aid of this condition, the formulation is performed in the frame of Dirac's canonical theory with constraints. Any physical quantity can be expressed in terms of constraint-independent canonical variables.
A microscopic theory of collective and independent-particle motions in many-fermion system is developed in the framework of Dirac's canonical theory with constraints.The basic idea is an extension of the conventional time-dependent Hartree-Fock theory based on the use of the Grassmann variables and, in certain sense, it supplements incomplete parts of the paper presented by the present authors.Canonicity condition to certify the canonical property of the variables, equation to determine collective submanifold and constraints to govern the collective and the Grassmann variables are given.