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

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 Kallen-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 behavior in the small and large coupling regimes.

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In this work, we derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, eta(0), using nonperturbative constraints in local scalar quantum field theories at finite temperature. As an example, we calculate eta(0) in the phi(4) theory and establish its leading behavior in the small and large coupling regimes.