Standard translation twists and an operator-bounded energy inequality

TL;DR

This paper explores standard twist operators in quantum field theory, revealing their unique properties in shifting operators between regions and deriving a new energy inequality involving smeared energy density.

Contribution

It explicitly computes twist operators for 2D chiral fermions and introduces a novel operator-bounded energy inequality based on these twists.

Findings

Twist operators can move operators between disjoint regions continuously.

Explicit formulas for twists in 2D chiral fermions are provided.

A new energy inequality bounds smeared energy density by an operator.

Abstract

Twist operators implement symmetries in bounder regions of the space. Standard twists are a special class of twists constructed using modular tools. The twists corresponding to translations have interesting special properties. They can move continuously an operator from a region to a disjoint one without ever passing through the gap separating the two. In addition, they have generators satisfying the spectrum condition. We compute explicitly these twists for the two dimensional chiral fermion field. The twist generator gives place to a new type of energy inequality where the smeared energy density is bounded below by an operator.