Non-Equilibrium Thermo Field Dynamics for Relativistic Complex Scalar and Dirac Fields

Details Non-Equilibrium Thermo Field Dynamics for Relativistic Complex Scalar and Dirac Fields Non-Equilibrium Thermo Field Dynamics for Relativistic Complex Scalar and Dirac Fields

2011-11-30

arxiv.org/abs/1111.7083v1

Physics

High Energy Physics

High Energy Physics - Theory

38 pages,2 figures

Scientific paper

Relativistic quantum field theories for complex scalar and Dirac fields are investigated in non-equilibrium thermo field dynamics. The thermal vacuum is defined by the Bogoliubov transformed creation and annihilation operators. Two independent Bogoliubov parameters are introduced for a charged field. Its difference naturally induces the chemical potential. Time-dependent thermal Bogoliubov transformation generates the thermal counter terms. We fix the terms by the self-consistency renormalization condition. Evaluating the thermal self-energy under the self-consistency renormalization condition, we derive the quantum Boltzmann equations for the relativistic fields.

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