  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.
