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.

这项工作致力于利用标量场的高阶导数对D = 1 + 3 维中的光前 Yukawa 模型进行量化。讨论了在存在约束的情况下计算狄拉克括号和相互作用场的（反）交换子代数的问题。利用狄拉克方法和高阶导数的奥斯特格拉斯基形式主义。获得具有相互作用和高阶导数的泛函狄拉克-伯格曼矩阵的逆的系统方法以两种变体形式介绍。对这两种变体的应用和细节进行了讨论。给出并分析了（反）换向器代数形式的量化结果。特别强调光锋 Yukawa 模型与高阶导数的相互作用结构。