Thermal Field Dynamics and Bialgebras

TL;DR

This paper demonstrates that thermal states in Thermal Field Dynamics can be derived from deformations of the extended Heisenberg bialgebra, eliminating the need for artificial redefinitions and supporting a fundamental role for bialgebras.

Contribution

It introduces a canonical method to obtain thermal representations from bialgebra deformations, unifying the approach across arbitrary dimensions.

Findings

Thermal states arise from restrictions of vacuum states on a doubled algebra.

Doubled Fock representations are derived from deformations of the extended Heisenberg bialgebra.

Bialgebra structures may be fundamental in Thermal Field Dynamics.

Abstract

In Thermal Field Dynamics, thermal states are obtained from restrictions of vacuum states on a doubled field algebra. It is shown that the suitably doubled Fock representations of the Heisenberg algebra do not need to be introduced by hand but can be canonically handed down from deformations of the extended Heisenberg bialgebra. No artificial redefinitions of fields are necessary to obtain the thermal representations and the case of arbitrary dimension is considered from the beginning. Our results support a possibly fundamental role of bialgebra structures in defining a general framework for Thermal Field Dynamics.