Spectral representation of the shear viscosity for local scalar QFTs at finite temperature

TL;DR

This paper derives a spectral representation for shear viscosity in local scalar QFTs at finite temperature, using non-perturbative constraints, and calculates it in  theory across different coupling regimes.

Contribution

It introduces a generalized spectral representation for shear viscosity based on non-perturbative constraints in thermal scalar QFTs and computes it explicitly in  theory.

Findings

Spectral representation for shear viscosity derived from non-perturbative constraints.

Explicit calculation of shear viscosity in  theory at different couplings.

Identification of the leading behavior of shear viscosity in small and large coupling limits.

Abstract

In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of the standard K\"{a}ll\'{e}n-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $\eta_{0}$. As an example, we calculate $\eta_{0}$ in $\phi^{4}$ theory, establishing its leading behaviour in the small and large coupling regimes.