Faddeev-Jackiw approach to hidden symmetries

Journal Article · Sun Oct 01 04:00:00 EDT 1995 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1995.1091· OSTI ID:166652

Wotzasek, C ^[1]

---

1. Univ. of Rochester, NY (United States)

The study of hidden symmetries within Dirac`s formalism does not possess a systematic procedure due to the lack of first-class constraints to act as symmetry generators. On the other hand, in the Fadeev-Jackiw approach, gauge and reparameterization symmetries are generated by the null eigenvectors of the sympletic matrix and not by constraints, suggesting the possibility of dealing systematically with hidden symmetries throughout this formalism. It is shown in this paper that indeed hidden symmetries of noninvariant or gauge fixed systems are equally well described by null eigenvectors of the sympletic matrix, just as the explicit invariances. The Faddeev-Jackiw approach therefore provide a systematic algorithm for treating all sorts of symmetries in an unified way. This technique is illustrated here by the SL(2,R) affine Lie algebra of the 2D induced gravity proposed by Polyakov, which is a hidden symmetry in the canonical approach of constrained systems via Dirac`s method, after conformal and reparameterization invariances have been fixed. 34 refs.

• OSTI ID: 166652
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 243; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DIRAC APPROXIMATION
FADDEEV EQUATIONS
LIE GROUPS
SYMMETRY