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

1996/02/27 by C. D. Fosco, T. Matsuyama, Fosco, C. D. +2
Biochemistry, Genetics and Molecular Biology · Chemistry · Engineering · Physics and Astronomy · #Advanced NMR Techniques and Applications #Electron Spin Resonance Studies #Particle Accelerators and Free-Electron Lasers #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9602142

23 pages, Latex

arxiv created 1996/02/27 · arxiv updated 2009/11/30

Abstract

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 θ_μ, 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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