IJPAM: Volume 79, No. 3 (2012)

A PURE DIRAC'S METHOD FOR YANG-MILLS EXPRESSED
AS A CONSTRAINED BF-LIKE THEORY

Alberto Escalante$^1$, J. Berra$^2$
$^1$Instituto de Física Luis Rivera Terrazas
Benemérita Universidad Autónoma de Puebla (IFUAP)
Apartado Postal J-48 72570 Puebla. Pue., MÉXICO
$^2$Facultad de Ciencias Fısico Matemáticas
Universidad Autónoma de Puebla
Apartado Postal 1152, 72001 Puebla, Pue., MÉXICO


Abstract. A pure Dirac's method of Yang-Mills expressed as a constrained $BF$-like theory is performed. In this paper we study an action principle composed by the coupling of two topological $BF$-like theories, which at the Lagrangian level reproduces Yang-Mills equations. By a pure Dirac's method we mean that we consider all the variables that occur in the Lagrangian density as dynamical variables and not only those ones that involve temporal derivatives. The analysis in the complete phase space enable us to calculate the extended Hamiltonian, the extended action, the constraint algebra, the gauge transformations and then we carry out the counting of degrees of freedom. We show that the constrained $BF$-like theory correspond at classical level to Yang-Mills theory. From the results obtained, we discuss briefly the quantization of the theory. In addition we compare our results with alternatives models that have been reported in the literature.

Received: April 19, 2012

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 79
Issue: 3