Non-equivalence of Faddeev-Jackiw method and Dirac-Bergmann algorithm and the modification of Faddeev-Jackiw method for keeping the equivalence

Journal Article · Mon Oct 15 04:00:00 EDT 2007 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2006.11.013· OSTI ID:21077647

Leng, Liao ^[1]; Yongchang, Huang ^[1]

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1. Institute of Theoretical Physics, Beijing University of Technology, Beijing 100022 (China)

From the angle of the calculation of constraints, we compare the Faddeev-Jackiw method with Dirac-Bergmann algorithm, study the relations between the Faddeev-Jackiw constraints and Dirac constraints, and demonstrate that Faddeev-Jackiw method is not always equivalent to Dirac method. For some systems, under the assumption of no variables being eliminated in any step in Faddeev-Jackiw formalism, except for the Dirac primary constraints, we are possible to get some Dirac secondary constraints which do not appear in the corresponding Faddeev-Jackiw formalism, which will result in the contradiction between Faddeev-Jackiw quantization and Dirac quantization. At last, accordingly, we propose a modified Faddeev-Jackiw method which keeps the equivalence between Dirac-Bergmann algorithm and Faddeev-Jackiw method. However, one point must be stressed that the Faddeev-Jackiw method and quantization in this paper is these mentioned in [J. Barcelos-Neto, C. Wotzasek, Mod. Phys. Lett. A 7 (1992) 1737], not the initial Faddeev-Jackiw method mentioned in [L. Faddeev, R. Jackiw, Phys. Rev. Lett. 60 (1988) 1692], which is completely on basis of Darboux transformation, and must have the elimination of variables in every step of that, so it is reasonable that the constraints in this Faddeev-Jackiw method is fewer than the Dirac secondary constraints. Thus, we overcome the difficulty of the Non-equivalence of the Faddeev-Jackiw method and Dirac-Bergmann algorithm, and make the equivalence of the Faddeev-Jackiw method and Dirac-Bergmann algorithm restored.

• OSTI ID: 21077647
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 10 Vol. 322; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
FADDEEV EQUATIONS
MODIFICATIONS
QUANTIZATION
TRANSFORMATIONS