Renormalization of Composite Operators in time-dependent Backgrounds

TL;DR

This paper investigates how composite operators are renormalized and mix in non-equilibrium systems lacking time-translation symmetry, revealing persistent non-local memory effects influenced by the system's mass scales.

Contribution

It introduces the concept of non-local memory-induced mixing of composite operators in out-of-equilibrium backgrounds, extending renormalization theory beyond equilibrium.

Findings

Composite operators exhibit non-local memory mixing.

Memory effects persist over timescales set by mass scales.

Renormalization in non-equilibrium involves non-local terms.

Abstract

We study the phenomenon of composite operator renormalization and mixing in systems where time-translational invariance is broken and the evolution is out-of-equilibrium. We show that composite operators mix also through non-local memory terms which persist for periods whose duration is set by the mass scales in the problem.