Light front quantization by Dirac's method

Commutation relations between fields and their conjugate momenta cannot be imposed on the light front x0 + x3 constant without any further consideration because, as a rule, canonical momenta are functions of the fields themselves rather than of the velocities leading to constraints between fields and momenta. To perform light front quantization, Dirac's method for the quantization of constrained systems is applied. Quantization is carried out through the Dirac bracket evaluated by means of constraints. An interesting relation between first-class constraints and boundary conditions is pointed out. Electrodynamics is quantized in a similar manner. If the gauge A+ = 0 is imposed, constraints become second class, subsidiary conditions do not arise but constraints modify the result of naive quantization in a definite way. (author)