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Perturbation theory including topological degrees of freedom: Yang-Mills theory in three Euclidean dimensions

E. Harikumar·Indrajit Mitra·H. S. Sharatchandra
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Abstract

A method for systematically including topological degrees of freedom in perturbation theory is developed. This is not bound by the restrictions of semi-classical techniques. The Yang-Mills theory in three Euclidean dimensions is considered here. A well-defined separation of the topological and the ``spin wave'' degrees of freedom is obtained, motivated by a singular gauge. This has ``photons'' distorting the spherically symmetric magnetic fields of Dirac monopoles, and massless charged vector bosons ``W'' scattering off the latter. It is explicitly shown that the Dirac string does not contribute. The mode of the charged vector bosons with total angular momentum J=0 provides precisely the core to give a finite energy to the monopole. The radial equation for W is remarkably simplified and only two polarization states survive exactly for the anomalous magnetic moment required by the Yang-Mills interaction.

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E. Harikumar, Indrajit Mitra, H. S. Sharatchandra. 2003-04-16. Perturbation theory including topological degrees of freedom: Yang-Mills theory in three Euclidean dimensions. https://arxiv.org/abs/hep-th/0304140

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