Stress-Energy Tensor and Ultraviolet Behaviour in Massive Integrable Quantum Field Theories

TL;DR

This paper investigates the short-distance behavior of massive integrable quantum field theories using form factors, revealing that different definitions of the stress-energy tensor lead to varied ultraviolet scaling behaviors.

Contribution

It demonstrates the compatibility of multiple stress-energy tensor definitions with on-shell dynamics and links these to distinct ultraviolet behaviors in the theories.

Findings

Different stress-energy tensor definitions affect UV scaling.

Presence of a non-zero matrix element $F_1$ influences behavior.

Ultraviolet behavior varies with the choice of $F_1$.

Abstract

The short distance behaviour of massive integrable quantum field theories is analyzed in terms of the form factor approach. We show that the on-shell dynamics is compatible with different definitions of the stress-energy tensor $T_{\mu\nu}(x)$ of the theory. In terms of form factors, this is equivalent to having a possible non-zero matrix element $F_1$ of the trace of $T_{\mu\nu}$ on one-particle state. Each choice of $F_1$ induces a different scaling behaviour of the massive theory in the ultraviolet limit.