Constraints and Interactions in Quantization of Yukawa Model with Higher Order Derivatives

TL;DR

This paper develops a systematic approach to quantize the light-front Yukawa model with higher order derivatives, addressing the complex Dirac brackets and commutator algebra in the presence of interactions and constraints.

Contribution

It introduces two variants for inverting the Dirac-Bergmann matrix in higher derivative interacting theories, advancing quantization methods for such models.

Findings

Explicit (anti-) commutator algebra for the model

Analysis of interaction structure with higher derivatives

Method for inverse Dirac-Bergmann matrix

Abstract

This work is dedicated to the quantization of the light-front Yukawa model in D=1+3 dimensions with higher order derivatives of the scalar field. The problem of the computing Dirac brackets and the (anti-) commutator algebra of interacting fields in the presence of the constraints is discussed. The Dirac method and the Ostrogradski formalism of the higher order derivatives are exploited. The systematic method of obtaining the inverse of the functional Dirac-Bergmann matrix with interactions and higher order derivatives is introduced in two variants. The discussion of applications and details of these two variants are conducted. The results of the quantization in the form of the (anti-) commutator algebra are presented and analyzed with special regard to the structure of the interactions for the light-front Yukawa model, which includes the higher order derivatives.