Correct Path-Integral Formulation of Quantum Thermal Field Theory in Coherent State Representation

The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in thecoherent-state representation. In doing this, we choose the thermal electrodynamics and ~4 theory as examples. Bythis quantization, correct expressions of the partition functions and the generating functionals for the quantum thermalelectrodynamics and ~4 theory are obtained in the coherent-state representation. These expressions allow us to performanalytical calculations of the partition functions and generating functionals and therefore are useful in practical appli-cations. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of thestationary-phase method. The generating functionals formulated in the position space are re-derived from the ones givenin the coherent-state representation.