The Problem of Ground State in Thermo-Field Dynamics

TL;DR

This paper examines the challenges of analytic continuation in quantum statistical physics, revealing that interactions cannot be neglected at infinite times, which impacts the formulation of Thermo-field dynamics.

Contribution

It demonstrates the necessity of including an interacting thermal vacuum in the real-time formalism due to singularities caused by adiabatic interaction vanishing.

Findings

Singularities at complex times affect analytic continuation.

Interacting thermal vacuum is essential for accurate real-time formalism.

Decoupling of interactions at infinite time is invalid.

Abstract

Analytic continuation of quantum statistical physics from imaginary to real time is analyzed. Adiabatic vanishing of interactions at real time infinities gives origin to singularities at complex times. This undermines the hypothesis of decoupling of interactions at $t \rightarrow \infty$. Hence an interacting thermal vacuum is a necessary component of the exact real-time formalism. Consequences for Thermo-field dynamics are discussed.