Time operator in QFT with Virasoro constraints

TL;DR

This paper introduces a novel approach to defining a self-adjoint time operator in quantum field theory by utilizing Virasoro constraints from string theory, offering a new perspective on Pauli's theorem.

Contribution

It demonstrates how Virasoro constraints enable the construction of a universal self-adjoint time operator in QFT, circumventing Pauli's theorem limitations.

Findings

Existence of a self-adjoint time operator in a specific subspace of Fock space.

The universal time operator can represent time in multiple subspaces.

New insights into the limitations imposed by Pauli's theorem.

Abstract

Time operator is studied on the basis of field quantization, where the difficulty stemming from Pauli's theorem is circumvented by borrowing ideas from the covariant quantization of the bosonic string, i.e., one can remove the negative energy states by imposing Virasoro constraints. Applying the index theorem, one can show that in a different subspace of a Fock space, there is a different self-adjoint time operator. However, the self-adjoint time operator in the maximal subspace of the Fock space can also represent the self-adjoint time operator in the other subspaces, such that it can be taken as the single, universal time operator. Furthermore, a new insight on Pauli's theorem is presented.