Constraints and interactions in quantization of Yukawa model with higher-order derivatives

This work is dedicated to quantization of the light-front Yukawa model in D = 1 + 3 dimensions with higher-order derivatives of a scalar field. The problem of computing Dirac brackets and the (anti-)commutator algebra of interacting fields in the presence of 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 quantization in the form of the (anti-)commutator algebra are presented and analyzed. There is a particular emphasis on the structure of interactions for the light-front Yukawa model with higher-order derivatives.