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Translations as gauge transformations

Published online by Cambridge University Press:  17 February 2009

P. K. Smrz
P. K. Smrz
Affiliation:
Department of Mathematics, University of Newcastle, New South Wales 2308, Australia
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Abstract

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A local description of space and time in which translations are included in the group of gauge transformations is studied using the formalism of fibre bundles. It is shown that the flat Minkowski space–time may be obtained from a non-flat connection in a de Sitter structured fibre bundle by choosing at least two different cross-sections. The interaction terms in the covariant derivative of a Dirac wave function that correspond to translations may be interpreted as the mass term of the Dirac equation, and then the two cross-sections (gauges) correspond to the description of a fermion and antifermion respectively.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 1 , June 1977 , pp. 38 - 45
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Kibble, T. W. B., “Lorentz invariance and the gravitational field”, J. Math, Phys. 2 (1961), 212–221.CrossRefGoogle Scholar
[2]Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, Vol. 1, Interscience, New York (1963).Google Scholar
[3]Smrz, P., “Gauge invariant interactions of classical fields”, J. Aust. Math. Soc. 19A (1975), 376–383.CrossRefGoogle Scholar
[4]Smrz, P., “Space–time and connections in Lie groups”, Proceedings of the International Symposium on Relativity and Unified Field Theory, Calcutta 1975–76.Google Scholar
[5]Trautman, A., “Fibre bundles associated with space-time”, Rep. Math. Phys. 1 (1970), 29–62.CrossRefGoogle Scholar
[6]Utiyama, R., “Invariant theoretical interpretation of interaction”, Phys. Rev. 101 (1955), 1597–1607.CrossRefGoogle Scholar