The C Operator in PT-Symmetric Quantum Field Theory Transforms as a Lorentz Scalar

TL;DR

This paper demonstrates that the C operator in PT-symmetric quantum field theory acts as a Lorentz scalar, extending the intrinsic parity operator and ensuring unitarity in non-Hermitian Hamiltonians with PT symmetry.

Contribution

It establishes that the C operator transforms as a Lorentz scalar, providing a deeper understanding of its role in PT-symmetric quantum field theory.

Findings

C operator is the complex extension of intrinsic parity

C transforms as a Lorentz scalar

Supports unitarity in PT-symmetric Hamiltonians

Abstract

A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator called C. It is shown here that C is the complex extension of the intrinsic parity operator and that the C operator transforms under the Lorentz group as a scalar.