Quantum $L^p$ inequalities in thermal states

TL;DR

This paper explores quantum $L^p$ inequalities in thermal states, showing that local densities are bounded below in a manner similar to quantum energy inequalities, with implications for thermal quantum field theory.

Contribution

It introduces quantum $L^p$ inequalities for local densities in thermal quantum fields, extending known vacuum inequalities to thermal states and specific spacetime geometries.

Findings

Local density bounded below in thermal states

Analogy to quantum energy inequalities in vacuum

Examples include Minkowski space and Rindler wedge

Abstract

In thermal quantum field theory, the global Liouvillian (the generator of time translations) is passive. How is this reflected in the properties of its local density, a quantum field? We propose that the locally averaged density is bounded below, but not above, with respect to the noncommutative $L^4$ norm. This is analogous to the known quantum energy inequalities in the vacuum situation. Our examples include thermal equilibrium on Minkowski space, and the Unruh effect on the Rindler wedge, both for the real scalar free field.