Implementation of conformal covariance by diffeomorphism symmetry

TL;DR

This paper constructs a global conformal symmetry representation for chiral conformal quantum theories, demonstrating covariance in all locally normal representations without energy positivity constraints.

Contribution

It provides a new, general method to implement conformal covariance via diffeomorphism symmetry, independent of energy positivity and applicable to all locally normal representations.

Findings

Constructed a unitary, strongly continuous conformal symmetry representation.

Showed the representation is inner in a global sense.

Applicable to all locally normal representations regardless of statistical dimension.

Abstract

Every locally normal representation of a local chiral conformal quantum theory is covariant with respect to global conformal transformations, if this theory is diffeomorphism covariant in its vacuum representation. The unitary, strongly continuous representation implementing conformal symmetry is constructed; it consists of operators which are inner in a global sense for the representation of the quantum theory. The construction is independent of positivity of energy and applies to all locally normal representations irrespective of their statistical dimensions (index).