Reply to "Comment on 'New ansatz for metric operator calculation in pseudo-Hermitian field theory '", arXiv:0906.4293

TL;DR

This paper defends a previously proposed ansatz for the metric operator in pseudo-Hermitian quantum field theory, demonstrating its validity in 3+1 dimensions and emphasizing its local and computationally compatible properties.

Contribution

It proves the validity of a metric operator ansatz in 3+1 dimensions, showing it is local and compatible with standard Feynman diagram calculations, countering prior sign error claims.

Findings

The ansatz is valid in 3+1 space-time dimensions.

The metric operator is local in the fields.

It allows standard Feynman diagram calculations.

Abstract

In this report, we reply to a recent comment by Carl M. Bender, Gregorio Benincasa and Hugh F. Jones on our work 'New ansatz for metric operator calculation in pseudo-Hermitian field theory (Phys. Rev. D. 79, 107702 (2009)). In fact, they figured out that there exist sign errors in our work which leaded to the conclusion of the invalidity of the ansatz introduced in our work. Here, we show that, the ansatz is valid in d+1 space-time dimensions, which by itself is a new and very important result. The importance of the work comes from the fact that it is the first time to have a metric operator for a quantum field theory which is local in the fields as well as valid in 3+1 space-time dimensions. Moreover, it is composed of the operators in the Hamiltonian itself which makes the Feynmann diagram calculations for the physical amplitudes go the same way as in conventional theories.