We use the improved Faddeev-Jackiw quantization method to quantize the electromagnetic field and its Lagrange multiplier fields. The method’s comparison with the usual Faddeev-Jackiw method and the Dirac method is given. We show that this method is equivalent to the Dirac method and also retains all the merits of the usual Faddeev-Jackiw method. Moreover, it is simpler than the usual one if one needs to obtain new secondary constraints. Therefore, the improved Faddeev-Jackiw method is essential. Meanwhile, we find the new meaning of the Lagrange multipliers and explain the Faddeev-Jackiw generalized brackets concerning the Lagrange multipliers.
According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transforma- tions of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was ob- tained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propaga- tors were obtained.
HUANG YongChang1,3,4, JIANG YunGuo1 & LI XinGuo2,3 1 Institute of Theoretical Physics, College of Applied Sciences, Beijing University of Technology, Beijing 100022, China
