Rudiments of Dual Feynman Rules for Yang-Mills Monopoles in Loop Space

Abstract

Dual Feynman rules for Dirac monopoles in Yang-Mills fields are obtained by the Wu-Yang (1976) criterion in which dynamics result as a consequence of the constraint defining the monopole as a topological obstruction in the field. The usual path-integral approach is adopted, but using loop space variables of the type introduced by Polyakov (1980). An anti-symmetric tensor potential $L_{\mu \nu }[\xi |s]$ appears as the Lagrange multiplier for the Wu-Yang constraint which has to be gauge-fixed because of the ``magnetic'' $\tilde{U}$-symmetry of the theory. Two sets of ghosts are thus introduced, which subsequently integrate out and decouple. The generating functional is then calculated to order $g^0$ and expanded in a series in $\tilde{g}$. It is shown to be expressible in terms of a local ``dual potential'' ${\tilde{A}}_{\mu }(x)$ found earlier, which has the same progagator and the same interaction vertex with the monopole field as those of the ordinary Yang-Mills potential $A_{\mu }$ with a colour charge, indicating thus a certain degree of dual symmetry in the theory. For the abelian case the Feynman rules obtained here are the same as in QED to all orders in $g$, as expected by dual symmetry.

21 pages, LateX, no figures

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Cited by in corpus (1)

• Nonabelian Generalization of Electric-Magnetic Duality - a Brief Review