Canonical Structure of the Non-Linear Sigma-Model in a Polynomial Formulation
| dc.creator | Fosco, C. D. | |
| dc.creator | Matsuyama, T. | |
| dc.date | 1996-02-27 | |
| dc.date.accessioned | 2026-07-07T04:21:54Z | |
| dc.date.available | 2026-07-07T04:21:54Z | |
| dc.description | 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 L_mu and a non-Abelian antisymmetric tensor field theta_{mu nu}, which constrains L_{mu} to be a `pure gauge' (F_{mu 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. | |
| dc.description | 20 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/hep-th/9602143 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9602143 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/54511 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Canonical Structure of the Non-Linear Sigma-Model in a Polynomial Formulation | |
| dc.type | text |