More on the operator-state map in non-relativistic CFTs

TL;DR

This paper develops an algebraic method to establish the operator-state correspondence in non-relativistic conformal field theories, paralleling the approach used in relativistic theories, by constructing an automorphism of the Schrödinger algebra.

Contribution

It introduces a novel algebraic construction of the operator-state map in non-relativistic CFTs using automorphisms of the Schrödinger algebra, inspired by relativistic methods.

Findings

Constructs an explicit automorphism of the Schrödinger algebra

Shows the construction parallels relativistic conformal theories

Provides a new algebraic framework for non-relativistic CFTs

Abstract

We propose an algebraic construction of the operator-state correspondence in non-relativistic conformal field theories by explicitly constructing an automorphism of the Schr\"odinger algebra relating generators in different frames. It is shown that the construction follows closely that of relativistic conformal field theories.