The SU(2) Non-Linear Sigma-Model in 2+1 Dimensions: Perturbation Theory in a Polynomial Formulation

Details The SU(2) Non-Linear Sigma-Model in 2+1 Dimensions: Perturbation Theory in a Polynomial Formulation The SU(2) Non-Linear Sigma-Model in 2+1 Dimensions: Perturbation Theory in a Polynomial Formulation

1996-02-27

arxiv.org/abs/hep-th/9602142v1

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, Latex

Scientific paper

We construct a perturbation theory for the SU(2) non-linear Sigma-model in 2+1 dimensions using a polynomial, first-order formulation, where the variables are a non-Abelian vector field L_mu (the left SU(2) current), and a non-Abelian pseudovector field $\theta_{\mu}$, which imposes the condition F_{mu nu}(L) = 0. The coordinates on the group do not appear in the Feynman rules, but their scattering amplitudes are easily related to those of the currents. We show that all the infinities affecting physical amplitudes at one-loop order can be cured by normal ordering, presenting the calculation of the full propagator as an example of an application.

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