Quantization of the Interacting Non-Hermitian Higher Order Derivative Field

TL;DR

This paper develops a method to quantize complex higher order derivative theories with interactions by mapping them to real theories using reality conditions, ensuring regularizability and renormalizability.

Contribution

It introduces a novel approach to quantize non-Hermitian higher order derivative theories through complex-to-real mappings with reality conditions.

Findings

The complex higher order theory can be mapped to a real theory using reality conditions.

The resulting real theory is shown to be regularizable.

The theory is renormalizable for certain interactions.

Abstract

The quantization of higher order time derivative theories including interactions is unclear. In this paper in order to solve this problem, we propose to consider a complex version of the higher order derivative theory and map this theory to a real first order theory. To achieve this relationship, the higher order derivative formulation must be complex since there is not a real canonical transformation from this theory to a real first order theory with stable interactions. In this manner, we work with a non-Hermitian higher order time derivative theory. To quantize this complex theory, we introduce reality conditions that allow us to map the complex higher order theory to a real one, and we show that the resulting theory is regularizable and renormalizable for a class of interactions.