Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-24T16:03:49.926Z Has data issue: false hasContentIssue false

Necessary and sufficient analytical conditions for the existence of false gauge field copies

Published online by Cambridge University Press:  08 July 2008

Adonai S. Sant' Anna
Affiliation:
Department of Mathematics, Federal University of Paraná, Curitiba, PR, 81531-990, Brazil, adonai@ufpr.br.
Get access

Abstract

Necessary and sufficient conditions for the existence of false gauge field copies by means of the Atiyah-Singer index theorem are established. Related topics are briefly discussed.

Type
Research Article
Copyright
Copyright © ISOPP 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Atiyah, M. F. and Singer, I. M.: The index of elliptic operators. Ann. Math. 87, 484530 (1968)CrossRefGoogle Scholar
2.Doria, F. A.: The geometry of gauge field copies. Comm. Math. Phys. 79, 435456 (1981)CrossRefGoogle Scholar
3.Freed, D. S. and Hopkins, M.: On Ramond-Ramond fields and K-theory. J. High Energy Phys. 5, Art. No. 044 (2000)Google Scholar
4.Gilkey, P. B.: The Index Theorem and the Heat Equation. Publish or Perish, Boston (1974)Google Scholar
5.Kobayashi, S. and Nomizu, K.: Foundations of Differential Geometry. Wiley, New York (1963)Google Scholar
6.Mayer, M. E.: Gauge Theories, Vector Bundles and the Index Theorem. Springer, Berlin (1981)Google Scholar
7.Sant' Anna, A. S., da Costa, N. C. A., and Doria, F. A.: The Atiyah-Singer index theorem and the gauge field copy problem. J. Phys. A: Math. Gen. 30, 55115516 (1997)CrossRefGoogle Scholar
8.Shanahan, P.: The Atiyah-Singer Index Theorem, an Introduction. Springer, Berlin (1978)CrossRefGoogle Scholar
9.Wu, T. T. and Yang, C. N.: Some remarks about unquantized non-Abelian gauge fields. Phys. Rev. D 12, 38433844 (1975)CrossRefGoogle Scholar