The Grassmannian Sigma Model in SU(2) Yang-Mills Theory

Abstract

Spin-charge separation in pure SU(2) Yang-Mills theory was recently found to involve the dynamics of an O(3) non-linear sigma model and, seemingly, a Grassmannian non-linear sigma model. In this article we explicitly construct the Grassmannian sigma model of the form appearing in the the spin-charge separated SU(2) theory through a quaternionic decomposition of the manifold, thus verifying its relevance in this context. The coupling between this model and the O(3) non-linear sigma model is further commented upon.

11 pages, undergraduate research project; version published in J. Phys. A

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Cited by in corpus (4)

• Embedding Brans-Dicke gravity into electroweak theory
• Integrability of the Einstein-nonlinear $SU(2)$ $\sigma$-model in a nontrivial topological sector
• Unifying Geometrical Representations of Gauge Theory
• On Lorentz Invariance, Spin-Charge Separation And SU(2) Yang-Mills Theory