4 × 4-matrix transformation for systems with spontaneous symmetry breakdown and self-consistent renormalization in nonequilibrium Thermo Field Dynamics

Making use of the thermo field dynamics (TFD) we formulate a calculable method for time-dependent nonequilibrium systems in a time representation (t-representation) rather than in the k0-Fourier representation. The corrected one-body propagator in the t-representation has the form of B−1 (diagonal matrix) B (B being a thermal Bogoliubov matrix). The number parameter in B here is the observed number (the Heisenberg number) with a fluctuation. With the usual definition of the on-shell self-energy a self-consistent renormalization condition leads to a kinetic equation for the number parameter. This equation turns out to be the Boltzmann equation, from which the entropy law follows.

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RENORMALIZATION AND BOLTZMANN EQUATIONS IN THERMAL QUANTUM FIELD THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x95000814 ◽

1995 ◽

Vol 10 (11) ◽

pp. 1693-1700 ◽

Cited By ~ 7

Author(s):

H. CHU ◽

H. UMEZAWA

Keyword(s):

Boltzmann Equation ◽

Renormalization Scheme ◽

Quantum Field Theories ◽

Quantum Field ◽

Boltzmann Equations ◽

Self Energy ◽

Spatially Inhomogeneous ◽

Thermo Field Dynamics ◽

Self Consistent ◽

Consistent Manner

The renormalization scheme in nonequilibrium thermal quantum field theories is reexamined. Instead of the self-energy diagonalization scheme, we propose to diagonalize Green’s function at equal time. This eliminates the problem of on-shell definition related to time-dependent energies and spatially inhomogeneous situations, and yields a Boltzmann equation that contains memory effect. The new diagonalization scheme and the derivation of the Boltzmann equation from it can be applied to any thermal situation. It allows the treatment of a nonequilibrium problem beyond perturbational calculations in a self-consistent manner. The results are applicable to both thermo field dynamics and the closed time path formalism.

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Classical solutions of a nonrelativistic model exhibiting spontaneous symmetry breakdown

Journal of Mathematical Physics ◽

10.1063/1.528412 ◽

1989 ◽

Vol 30 (2) ◽

pp. 464-469

Author(s):

D. Spehler ◽

G. C. Marques

Keyword(s):

Classical Solutions ◽

Symmetry Breakdown ◽

Nonrelativistic Model ◽

Spontaneous Symmetry Breakdown

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CLEAN PRECISION TESTS OF THE ELECTROWEAK THEORY

Modern Physics Letters A ◽

10.1142/s0217732392000902 ◽

1992 ◽

Vol 07 (12) ◽

pp. 1009-1021 ◽

Cited By ~ 5

Author(s):

ZENRŌ HIOKI

Keyword(s):

Experimental Data ◽

Top Quark ◽

Higgs Mass ◽

Quantum Correction ◽

Electroweak Theory ◽

Weak Boson ◽

Yukawa Couplings ◽

Symmetry Breakdown ◽

Electroweak Precision ◽

Spontaneous Symmetry Breakdown

Present status of electroweak precision tests via the weak boson masses is reviewed, emphasizing that the standard SU(2) × U(1) theory is phenomenologically very successful also at quantum correction level. In particular, it is shown that the latest experimental data indicate the existence not only of the whole one-loop corrections but also of the non-decoupling top-quark effects, independent of the Higgs mass, which are a characteristic feature of theories with masses generated by spontaneous symmetry breakdown plus large Yukawa couplings.

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UNIFIED ELECTROWEAK MODEL BASED ON SPACE–TIME AND ISOSPIN SYMMETRIES

International Journal of Modern Physics A ◽

10.1142/s0217751x05019452 ◽

2005 ◽

Vol 20 (01) ◽

pp. 175-198 ◽

Cited By ~ 2

Author(s):

D. SPEHLER ◽

G. C. MARQUES

Keyword(s):

Degrees Of Freedom ◽

Space Time ◽

Scalar Particles ◽

Symmetry Breakdown ◽

Vector Bosons ◽

Rank 2 ◽

Electroweak Model ◽

Spontaneous Symmetry Breakdown ◽

Internal Degrees Of Freedom

We propose a spinorial approach to the unified electroweak interactions, in which no use is made of spontaneous symmetry breakdown. No scalar particles are needed in order to break the symmetry. No reference is made to gauge symmetry. Our approach stresses the role of space–time and isospin symmetries in the build up of the electroweak model. Internal degrees of freedom, such as isospin, are incorporated in the theory by using spinors carrying isospin indices. All vector bosons are described by a rank 2 field in the spinorial and the isospinorial indices. Leptons are accomodated in a rank 1 spinor field and in a rank 2 isospin field as well. The dynamical variables of the theory are the chiral and isochiral components of these fields.

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