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Rudiments of Dual Feynman Rules for Yang-Mills Monopoles in Loop Space
High Energy Physics - Theory · Submitted 28 Mar 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is shown to be expressible in terms of a local ``dual potential'' $\widetilde{A}_\mu (x)$ 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.
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The abstract, sentence by sentence
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'' $\widetilde{U}$-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 $\widetilde{g}$. It is shown to be expressible in terms of a local ``dual potential'' $\widetilde{A}_\mu (x)$ 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.64 | 0.63 | 0.22 | asserted 1.00 |
| s1 | The usual path-integral approach is adopted, but using loop space variables of the type introduced by Polyakov (1980). | method 0.99 | 0.74 | 0.03 | asserted 0.99 |
| s2 | 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'' $\widetilde{U}$-symmetry of the theory. | method 0.94 | 0.69 | 0.05 | asserted 1.00 |
| s3 | Two sets of ghosts are thus introduced, which subsequently integrate out and decouple. | method 0.98 | 0.84 | 0.03 | asserted 1.00 |
| s4 | The generating functional is then calculated to order $g^0$ and expanded in a series in $\widetilde{g}$. | method 0.96 | 0.91 | 0.05 | asserted 0.99 |
| s5 | It is shown to be expressible in terms of a local ``dual potential'' $\widetilde{A}_\mu (x)$ 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. | result 0.80 | 0.85 | 0.68 | asserted 0.60 |
| s6 | 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. | result 0.86 | 0.76 | 0.22 | asserted 1.00 |
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Original 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'' $\widetilde{U}$-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 $\widetilde{g}$. It is shown to be expressible in terms of a local ``dual potential'' $\widetilde{A}_\mu (x)$ 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.
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