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.

中文翻译：

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关于光前汤川模型相互作用的狄拉克-伯格曼过程

在这项工作中，我们应用 Dirac-Bergmann 程序来建立狄拉克括号，它考虑了 D=1+3 维中光前汤川模型的相互作用。我们使用了一个简单的矩阵方程来解决设置任务，其中主要问题是计算由启用交互的约束组成的数组的逆矩阵。建议的设备归结为某些基本矩阵系列的使用。获得的结果 - 狄拉克括号包括 Yukawa 模型的相互作用 - 包含与费米子 - 标量耦合常数的一阶和二阶幂的相互作用贡献。从物理角度讨论量子化后光前超表面上相互作用理论的（反）换向器的结构和性质是很有趣的。我们将获得的结果与从海森堡方程推断出的量化改进方法的计算进行了比较。未解决的问题是由约束生成的逆矩阵是否给出了所研究问题的完整和精确或仅近似解。