1996/02/27 by C. D. Fosco, T. Matsuyama, Fosco, C. D. +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9602143
20 pages, Latex
arxiv created 1996/02/27 · arxiv updated 2009/11/30
We study the canonical structure of the SU(N) non-linear Sigma-model in a polynomial, first-order representation. The fundamental variables in this description are a non-Abelian vector field Lmu and a non-Abelian antisymmetric tensor field thetamu nu, which constrains Lmu to be a `pure gauge' (Fmu nu(L) = 0) field. The second-class constraints that appear as a consequence of the first-order nature of the Lagrangian are solved, and the reduced phase-space variables explicitly found. We also treat the first-class constraints due to the gauge-invariance under transformations of the antisymmetric tensor field, constructing the corresponding most general gauge-invariant functionals, which are used to describe the dynamics of the physical degrees of freedom. We present these results in 1+1, 2+1 and 3+1 dimensions, mentioning some properties of the (d+1)-dimensional case. We show that there is a kind of duality between this description of the non-linear σ-model and the massless Yang-Mills theory. This duality is further extended to more general first-class systems.