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Modern Physics Letters B

NEW APPLICATIONS OF <η| REPRESENTATION IN THERMAL FIELD STATISTICS

Hong-Yi Fan, Hui Wang

Published Jun 30, 2000• 7 citations
Publisher

Abstract

We derive <η| representation of density matrices ρ for radiation fields, where <η| is the newly established coherent thermal state [H.-Y. Fan and Y. Fan, Phys. Lett.A246, 242 (1998)] in thermal field dynamics. We then apply <η|ρ> to calculate thermal averages and develop the theory for the quantum phase space distributions. We also study the quantum master equations in the <η| representation and find it has similar evolving property to the coherent representation of a pure state.

DOI
10.1142/s0217984900000707

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We derive <η| representation of density matrices ρ for radiation fields, where <η| is the newly established coherent thermal state [H.-Y. Fan and Y. Fan, Phys. Lett.A246, 242 (1998)] in thermal field dynamics. We then apply <η|ρ> to calculate thermal averages and develop the theory for the quantum phase space distributions. We also study the quantum master equations in the <η| representation and find it has similar evolving property to the coherent representation of a pure state.
The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and ψ4 theory as examples. By this quantization, correct expressions of the partition functions and the generating functionals for the quantum thermal electrodynamics and ψ4 theory are obtained in the coherent-state representation. These expressions allow us to perform analytical calculations of the partition functions and generating functionals and therefore are useful in practical applications. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of the stationary-phase method. The generating functionals formulated in the position space are re-derived from the ones given in the coherent-state representation.
The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and φ 4 theory as examples. By this quantization, correct expressions of the partition functions and the generating functionals for the quantum thermal electrodynamics and φ 4 theory are obtained in the coherent-state representation. These expressions allow us to perform analytical calculations of the partition functions and generating functionals and therefore are useful in practical applications. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of the stationary-phase method. The generating functionals formulated in the position space are re-derived from the ones given in the coherent-state representation.
Quantum Statistical Mechanics of interaction systems of atom radiation field is formulated by the use of the representation of coherent state direct prduct. After introducing a newly defined distribution of interaction syetems, the Bloch equation for the equilibrium density matrix is converted into partial differential equation of the type of separating variables. Formal solution of this differential equation is presented. and operator which is composed of a +,a, and its average formula are written down in the present representation.