Decomposing Theory Of Gauge Potential And Canonical Quantization In General QED System

A general QED system is described by a singular Lagrangian and is subject tosome inherent constraints in phase space. For this system, the standard quantizationmethods cannot be used any more. Although the quantization of this system has beenachieved, it is not perfect.The general QED system is such a system that Maxwell field coupling withFermi field, that is to say, in this system there exist distributions of charges andcurrents. The distribution of charges and currents makes the general QED systemdiffer from the free Maxwell field in which the physical effects of scalar andlongitudinal photons cancel out each other, explicitly say, the longitudinal and scalarphotons can produce observable effects, such as Coulomb force, in the presences ofcharge or current distributions. And the observable effects should be guaranteed bythe gauge invariance of the general QED system. But in the traditional Coulombgauge, the gauge invariance of the general QED system cannot keep any more,because the longitudinal component of gauge potential is reduced to zero, whichmeans that the traditional Coulomb gauge is not ideally chosen for quantizing thegeneral QED system. While Lorentz gauge is also not ideal for the quantization,because there are the negative probabilities caused by the scalar photons and thecanonical quantization is very complicated. Naturally, a dilemma is caused, i.e., howto restore the gauge invariance of the general QED system and facilitate thequantization.In this thesis, we give an excellent solution to the canonical quantization of thegeneral QED system. Not only the gauge invariance of the general QED systemrestores, but also the results of quantization are consistent with that in the traditionalCoulomb gauge. Moreover, no nonphysical factors produced as in Lorentz gauge. Themethod of this thesis utilized just is the decomposition of gauge potential. Under thedecomposed gauge potential, we don’t take account into the natural transverse fieldcondition and directly deduce the inherent constraints of the general QED system.Also, we investigate the motion equations and discover some new relationships.