Canonical Structure of the Non-Linear σ-Model in a Polynomial Formulation

概要

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We study the canonical structure of the SU(N) non-linear σ-model in a polynomial, first-order representation. The fundamental variables in this description are a non-Abelian vector field L_μ and a non-Abelian antisymmetric tensor field θ_<μν>, which constrains L_μ to be a 'pure gauge' (F_<μν>(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 are 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+l-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.
理論物理学刊行会の論文
1995-02-25