Rigorous bounds on transport from causality

TL;DR

This paper uses causality principles to establish universal bounds on dispersion relations and transport coefficients in relativistic quantum field theories, including an upper limit on diffusivity.

Contribution

It provides the first rigorous bounds on transport coefficients derived from causality constraints in quantum field theories.

Findings

Causal dispersion relations have a finite radius of convergence.

Universal bounds are established for all transport coefficients.

An upper bound on diffusivity is derived.

Abstract

We use causality to derive a number of simple and universal constraints on dispersion relations, which describe the location of singularities of retarded two-point functions in relativistic quantum field theories. We prove that all causal dissipative dispersion relations have a finite radius of convergence. We then give two-sided bounds on all transport coefficients in units of this radius, including an upper bound on diffusivity.