Yoshiya Yamanaka

Canonical formalism of dissipative fields in thermo field dynamics

For the stationary case the canonical formalism of thermally dissipative fields with both positive‐ and negative‐frequency parts is constructed. This formulation enables one to follow the self‐consistent renormalization scheme which creates the dissipation spontaneously. The self‐interacting φ3 model is examined as an example of the spontaneous creation of dissipation. The parameter α appearing in the thermal state conditions as well as observables independent of the choice of α are discussed.

Relation Between Quantum and Thermal Fluctuations

Abstract A relation between quantum and thermal fluctuations, called the generalized uncertainty relation, is derived and discussed. It is given in the terminology of thermo field dynamics. The relation enables us to separate the purely thermal fluctuation from the total fluctuation.

Time‐dependent canonical formalism of thermally dissipative fields and renormalization scheme

The canonical formalism of thermally dissipative semifree fields in the time‐dependent situation is presented. The use of thermal covariant derivatives simplifies the formulation considerably. With this formalism one can unambiguously obtain the interaction Hamiltonian under any thermal situation which together with the free propagator enables perturbative calculations to be performed. The ‘‘on‐shell’’ renormalization condition in the time‐dependent case is also discussed. The model of a system with a thermal reservoir illustrates how the present formalism works in time‐dependent situations.

Spontaneous creation of dissipation in thermo field dynamics and its examples

This article reviews the formulation of the self-consistent renormalization method in thermo field dynamics and the way this can lead to the spontaneous creation of dissipation in an isolated system. The general theory is illustrated by an explicit solution of a model of a system interacting with a reservoir, and is also applied to a relativistic self-interacting scalar model. The appearance of dissipation is shown. We also compare thermo field dynamics with the path-ordering formalism of Schwinger and Keldysh and the Liouville equation formalism.

Coherent and thermal coherent state

The characterization of coherent states as the quantum states that split into two uncorrelated beams is considered. The characterization leads to the study of coherent states at finite temperature—thermal coherent states (TCS’s). These TCS’s are defined within the formalism of thermo field dynamics (TFD). TFD allows a generalization of the uncertainty relation that accounts for both thermal and quantum fluctuations. The TCS is shown to be a minimal state for the generalized uncertainty relation.

Thermal degree of freedom in thermo field dynamics

The view of the thermal degree of freedom for the quantum field system, using the language of thermo field dynamics, is elaborated in this paper: the thermal degree of freedom is the degree of freedom to move through degenerate thermal vacua associated with spontaneous breakdown of a certain symmetry (Ĝ-symmetry). Based on this view, we study a quasi-particle picture, in which the Ĝ-transformation becomes the thermal Bogoliubov transformation.

Heisenberg and interaction representations in thermo field dynamics

In this paper the so‐called α degree of freedom appearing in thermal quantum field theory is discussed, using thermo field dynamics (TFD). This paper is confined to stationary thermal situations, both nonequilibrium and equilibrium. The main result is that when the stationary number distribution differs from the equilibrium one the use of time ordered and antitime ordered formalisms picks up α=1 and α=0, in contrast to the general belief that the Feynman diagram method is usable for any other α as well. This situation in TFD will be compared with the other approaches. The reason why the Feynman diagram method becomes available for any α in the case of the equilibrium distributions is also studied.

THERMO FIELD DYNAMICS IN TIME REPRESENTATION

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.

TEMPORAL DESCRIPTION OF THERMAL QUANTUM FIELDS

By making use of time-dependent Bogoliubov transformations, we develop a calculation technique for time-dependent non-equilibrium systems of quantum fields in a time-representation (t-representation). The corrected one-body propagator in the t-representation turns out to have the form B−1 (diagonal matrix) B (B being a thermal Bogoliubov matrix). Applying the usual on-shell concept to the diagonal matrix part of the self-energy, we formulate a self-consistent renormalization scheme. This renormalization determines the vacuum and leads to a kinetic equation for the number density parameter, which reduces to the Boltzmann equation in the lowest approximation. This gives us the increasing entropy in time (the second law of thermodynamics).

Thermodynamics and quantum field theory

Abstract We describe the thermal change of a quantum field system using thermo field dynamics, an operator quantum theory. With this it is straightforward to discuss the change in thermal energy which we relate to thermodynamics. The fundamental concept is that it is necessary to recognize two sources of time dependence, one for the Heisenberg operators and one for the Heisenberg states; this is a radical departure from conventional quantum field theory and one that should find many applications.