Scalar Quantum Field Theory with Cubic Interaction

TL;DR

This paper demonstrates that an i phi^3 quantum field theory is physically consistent, with a positive spectrum and unitarity, by constructing a new operator C that defines the inner product in PT-symmetric quantum field theory.

Contribution

It introduces a perturbative method to construct a C operator in PT-symmetric quantum field theory, establishing the physical acceptability of the i phi^3 model.

Findings

The i phi^3 field theory has a positive spectrum.

The theory is shown to be unitary.

A new, time-independent C operator is constructed.

Abstract

In this paper it is shown that an i phi^3 field theory is a physically acceptable field theory model (the spectrum is positive and the theory is unitary). The demonstration rests on the perturbative construction of a linear operator C, which is needed to define the Hilbert space inner product. The C operator is a new, time-independent observable in PT-symmetric quantum field theory.