Quantization of hamiltonian with complex form

[Nixom]

In most of textbooks, the canonical quantization procedure is used to quantize the hamiltonian with a simple form, the quadratic form. I just wonder how should we deal with more complex form hamiltonian, such like the ones including interaction terms?

 

[Bill_K]

Bjorken and Drell Vol II discusses canonical quantization of spinor electrodynamics in the chapter "Interacting Fields". Since the fields are no longer free fields, they don't have plane wave solutions, so instead of four-dimensional Fourier transforms they do a three-dimensional Fourier expansion at t = 0. The operator expansion coefficients are assigned the same commutation relations as for free fields, and then show the relations continue to hold for all t.

"The operator expansion coefficients, however, no longer retain their simple physical interpretations as creation and destruction operators for single quanta of given definite masses".