Jan Żochowski | Searcharxiv

arXiv2022

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

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.

hep-th↗

arXiv2020

Dirac-Bergmann Procedure Having Regard to Interaction for Light-Front Yukawa Model

In this work we applied the Dirac-Bergmann procedure to establish the Dirac brackets, which have regard to interaction for the light-front Yukawa model in D=1+3 dimensions. We made use of a simple matrix equation leading to solution of the set task, wherein the main problem was to calculate the inverse matrix to the array composed of the constraints for enabled interaction. Proposed device comes down to the usage of certain, rather elementary matrix series. Obtained result - Dirac brackets including interaction for the Yukawa model - embraces the interacting contributions with first and second powers of the fermionic - scalar coupling constant. It is interesting from the physical point of view for discussion on the structure and the properties of the (anti-) commutators of the interacting theories on the light-front hyper-surface after quantization. We compared obtained results to the computations coming from modified method of the quantization, inferred from the Heisenberg equations. The open problem is whether the inverse matrix to this one, generated by the constraints, gives the complete and exact or only approximate solution of the studied problem.

hep-th↗