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.
Highlights
Determining the properties of quantum field theories (QFTs) at finite temperature is essential for describing many physical phenomena
In local scalar quantum field theories at finite temperature correlation functions are known to satisfy certain nonperturbative constraints, which for two-point functions in particular implies the existence of a generalization of the standard Källen-Lehmann representation
Local formulations of QFT at finite temperature imply the existence of nonperturbative constraints on the structure of thermal correlation functions
Summary
Determining the properties of quantum field theories (QFTs) at finite temperature is essential for describing many physical phenomena. Temporal invariance is implied by the fact that jΩβi is an equilibrium state, and stationary, whereas spatial translational and rotational invariance is a choice that assumes the thermal system to be both homogeneous and isotropic [4] Despite these differences, there are several key assumptions that remain unchanged, including the distributional nature of the fields, their locality, and the fact that the states in the theory are constructed by acting with the fields on the. The remainder of this paper is structured as follows: in Sec. II we outline the general nonperturbative constraints imposed on thermal correlation functions, in particular the two-point function of real scalar fields; in Sec. III we use these constraints to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states η0, which in Sec. IV we apply in order to calculate an explicit expression for η0 in φ4 theory.
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