Quantization of a Complex Higher Order Derivative Theory using Path Integrals

TL;DR

This paper develops a method to quantize a complex higher order derivative theory via path integrals, addressing issues like unbounded energy and negative norm states by extending to the complex plane and imposing reality conditions.

Contribution

It introduces a novel approach to quantize higher order derivative theories using complex path integrals, with a consistent complex structure and reality constraints.

Findings

Successfully extended the theory to the complex plane

Constructed a consistent complex path integral measure

Demonstrated the renormalizability of the projected real theory

Abstract

This work addresses the quantization of a self-interacting higher order time derivative theory using path integrals. To quantize this system and avoid the problems of energy not bounded from below and states of negative norm, we observe the following steps: 1) We extend the theory to the complex plane and in this sense we double the degrees of freedom. 2) We add a total derivative to fix the convenient boundary conditions. 3) We check that the complex structure is consistent. 4) To map from the complex space to the real space we introduce reality conditions as second class constraints and we check that the interactions do not generate more constraints. 5) We built the measure of the complex path integral and we show that including currents the theory is projected to a self-interacting real theory that is renormalizable.