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U(\(N\)) Yang-Mills in non-commutative space time. (English) Zbl 1415.83031
Summary: We present an approach to \( \mathrm{U}_{\ast}(N) \) Yang-Mills theory in non-commutative space based upon a novel phase-space analysis of the dynamical fields with additional auxiliary variables that generate Lorentz structure and colour degrees of freedom. To illustrate this formalism we compute the quadratic terms in the effective action focusing on the planar divergences so as to extract the \({\beta}\)-function for the Yang-Mills coupling constant. Nonetheless the method presented is general and can be applied to calculate the effective action at arbitrary order of expansion in the coupling constant and is well suited to the computation of low energy one-loop scattering amplitudes.
83C65 Methods of noncommutative geometry in general relativity
70S15 Yang-Mills and other gauge theories in mechanics of particles and systems
81T10 Model quantum field theories
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