Faddeev-Senjanovic Quantization of the Supersymmetrical Electrodynamic System

JIANG Yun-Guo; HUANG Yong-Chang

Chinese Physics C> 2006, Vol. 30> Issue(12) : 1151-1155

Faddeev-Senjanovic Quantization of the Supersymmetrical Electrodynamic System

JIANG Yun-Guo ,
HUANG Yong-Chang ^,

Institute of Theoretical Physics, College of Applied Mathematics and Physics,Beijing University of Technology, Beijing 100022, China2 Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, China3 CCAST World Lab., Beijing 100080, China

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Abstract：
According to the method of path integral quantization for the canonical constrained system in Faddeev-Senjanovic scheme, we quantize the supersymmetrical electrodynamic system in general situation, and obtain the generating functional of Green function. Another first class constraint is obtained by making the linear combination of several primary constraints, the generator of gauge transformation is constructed, gauge transformations of all the different fields are deduced. Utilizing the consistency equation of gauge fixing condition to deduce another gauge fixing condition, we find that the secondary constraint of the system is an Euler-Lagrange equation which is just the conversation law of electric charge. Thus, we do not need to calculate the other secondary constraints step by step, and get no new constraints naturally. So, the Faddeev-Senjanovic path integral quantization of the supersymmetrical electrodynamic system is simplified.

References

[1]

. Kushreshtha D S, Muller-Kirsten H J W. Phys. Rev., 1991,D43: 33762. Batalin I A, Bering K, Damgaard P H. Nucl. Phys., 1998,B515: 4553. Rupp C, Scharf R, Sibold K. Nucl. Phys., 2001, B612: 3134. Muller-Kirsten H J W, Wiedemann A. Supersymmetry-An Introduction with Conceptual and Calculational Details. Singapore: World Scientifc, 1987. 5475. Muller-Kirsten H J W, Wiedemann A. Supersymmetry-An Introduction with Conceptual and Calculational Details. Singapore: World Scientifc, 1987. 5466. Dirac P A M. Lecture on Quantum Mechanics. New York:Yeshiva University, 1964. 1-117. Dirac P A M. Lecture on Quantum Mechanics. New York:Yeshiva University, 1964. 98. LI Zi-Ping. Symmetries in Constrained Canonical System.Beijing: Science Press, 2002. 219. Dirac P A M. Lecture on Quantum Mechanics. New York:Yeshiva University, 1964. 1-1710. Castellani L. Ann. Phys.(NY), 1983, 144: 35711. Senjanovic P. Ann. Phys.(NY), 1976, 100: 22712. Costa M E V, Girotti H O, Simoes T J M. Phys. Rev.,1985, D32: 4013. LIAO Leng, HUANG Yong-Chang. HEP NP, 2006, 30:191(in Chinese)(廖棱, 黄永畅. 高能物理与核物理, 2006, 30: 191)

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JIANG Yun-Guo and HUANG Yong-Chang. Faddeev-Senjanovic Quantization of the Supersymmetrical Electrodynamic System[J]. Chinese Physics C, 2006, 30(12): 1151-1155.

JIANG Yun-Guo and HUANG Yong-Chang. Faddeev-Senjanovic Quantization of the Supersymmetrical Electrodynamic System[J]. Chinese Physics C, 2006, 30(12): 1151-1155. shu

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Received: 2006-03-06
Revised: 2006-04-12

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Faddeev-Senjanovic Quantization of the Supersymmetrical Electrodynamic System

JIANG Yun-Guo
HUANG Yong-Chang ^,

Corresponding author: HUANG Yong-Chang,

Institute of Theoretical Physics, College of Applied Mathematics and Physics,Beijing University of Technology, Beijing 100022, China2 Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, China3 CCAST World Lab., Beijing 100080, China

Received Date: 2006-03-06
Accepted Date: 2006-04-12
Available Online: 2006-12-05

Abstract: According to the method of path integral quantization for the canonical constrained system in Faddeev-Senjanovic scheme, we quantize the supersymmetrical electrodynamic system in general situation, and obtain the generating functional of Green function. Another first class constraint is obtained by making the linear combination of several primary constraints, the generator of gauge transformation is constructed, gauge transformations of all the different fields are deduced. Utilizing the consistency equation of gauge fixing condition to deduce another gauge fixing condition, we find that the secondary constraint of the system is an Euler-Lagrange equation which is just the conversation law of electric charge. Thus, we do not need to calculate the other secondary constraints step by step, and get no new constraints naturally. So, the Faddeev-Senjanovic path integral quantization of the supersymmetrical electrodynamic system is simplified.