From Classical Mechanics with Doubled Degrees of Freedom to Quantum Field Theory for Nonconservative System

TL;DR

This paper demonstrates that a classical mechanics framework with doubled degrees of freedom can be extended to quantum field theory, providing a natural connection to nonequilibrium Thermo Field Dynamics and explaining the matrix structure of Green's functions.

Contribution

It extends Galley's Hamilton's principle for nonconservative classical systems to quantum field theory, linking it to nonequilibrium Thermo Field Dynamics.

Findings

The doubled degrees of freedom formalism applies to quantum fields.

The resulting quantum theory matches nonequilibrium Thermo Field Dynamics.

The matrix structure of Green's functions is explained by this formalism.

Abstract

The $2 \times 2$-matrix structure of Green's functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton's principle with initial data for nonconservative classical systems, doubling each degree of freedom [Phys. Rev. Lett. 110, 174301 (2013)]. We show that the Galley's Hamilton formalism can be extended to quantum field and that the resulting theory is naturally identical with nonequilibrium TFD.