Faddeev-Jackiw quantization and constraints

Journal Article · Mon Aug 10 04:00:00 EDT 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X9200226X· OSTI ID:7135153

Barcelos-Neto, J; Wotzasek, C ^[1]

---

1. Universidade Federal Rural do Rio de Janeiro, RJ (Brazil). Dept. de Fisica

In a recent Letter, Faddeev and Jackiw have shown that the reduction of constrained systems into its canonical, first-order form, can bring some new insight into the research of this field. For sympletic manifolds the geometrical structure, called Dirac or generalized bracket, is obtained directly from the inverse of the nonsingular sympletic two-form matrix. In the cases of nonsympletic manifolds, this two-form is degenerated and cannot be inverted to provide the generalized brackets. This singular behavior of the sympletic matrix is indicative of the presence of constraints that have to be carefully considered to yield to consistent results. One has two possible routes to treat this problem: Dirac has taught us how to implement the constraints into the potential part (Hamiltonian) of the canonical Lagrangian, leading to the well-known Dirac brackets, which are consistent with the constraints and can be mapped into quantum commutators (modulo ordering terms). The second route, suggested by Faddeev and Jackiw, and followed in this paper, is to implement the constraints directly into the canonical part of the first order Lagrangian, using the fact that the consistence condition for the stability of the constrained manifold is linear in the time derivative. This algorithm may lead to an invertible two-form sympletic matrix from where the Dirac brackets are readily obtained. This algorithm is used in this paper to investigate some aspects of the quantization of constrained systems with first- and second-class constraints in the sympletic approach.

• OSTI ID: 7135153
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 20; ISSN IMPAEF; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
CANONICAL TRANSFORMATIONS
COMMUTATION RELATIONS
CONSTRAINTS
DIRAC OPERATORS
EQUATIONS
FADDEEV EQUATIONS
FIELD THEORIES
FUNCTIONS
GEOMETRY
HAMILTONIANS
LAGRANGIAN FUNCTION
MAPPING
MATHEMATICAL LOGIC
MATHEMATICAL MANIFOLDS
MATHEMATICAL OPERATORS
MATHEMATICS
MATRICES
QUANTIZATION
QUANTUM OPERATORS
SINGULARITY
TRANSFORMATIONS