I see in many textbooks that all authors start field quantization with EM field confined in a cube of finite size, certainly some B.C. is imposed, usually periodic B.C., finally the cube goes to whole space. I have some questions on this procedure: 1, Is periodic(or other) B.C. reasonable? Doesn't the B.C. have any influence on final results? 2, Is this cube necessary? Why not just do the decomposition in the whole space(continuous decompostition spectrum encounterd?)? I heared that this method of quantizing EM field was originally proposed by Dirac in his Lectures on Quantum Field Theory. Would anyone be kind enough to share it? Thank you all for attention!
Periodic and box boundry conditions lead to discrete energies. They have been used in virtually all branches of physics, to simplify some of the problems associated with continuous spectra. You can find discussions of this in virtually any text on QM or QFT -- this trick goes back many, many years, before 1900, for many types of boundary value problems as well. These days, working directly with the continuous spectra is more in vogue. Regards, Reilly Atkinson.
Box quantization for the EM field simply is a nice way to get to the concept of "photon" by evading the headaches one gets when he tries to quantize a gauge classical field theory described in [itex] \mathbb{M}_{4} [/itex]. Daniel.