Spacelike thermal correlators are almost time-independent

TL;DR

This paper demonstrates that in relativistic thermal field theories, spacelike-separated correlators exhibit near time-independence, with classical cases showing complete time independence under spacelike separation.

Contribution

It establishes a quantitative understanding of the near time-independence of spacelike thermal correlators in relativistic and classical thermal field theories.

Findings

Correlators are exponentially weakly dependent on time at spacelike separation.

Time dependence vanishes entirely in classical thermal field theory for spacelike points.

Provides insight into the temporal behavior of thermal correlators in relativistic regimes.

Abstract

We show that, in relativistic field theories, the thermal correlation function of N bosonic operators <O_1(x_1,t_1) O_2(x_2,t_2) .. O_N(x_N,t_N)> at sufficiently spacelike-separated points shows exponentially weak dependence on the time variables t_1,...,t_N, when the space separations are held fixed. For classical thermal field theory, the time dependence vanishes when all points are spacelike separated