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Fibre bundles and Yang-Mills fields

Published online by Cambridge University Press:  09 April 2009

P. K. Smrz
P. K. Smrz
Affiliation:
The University of NewcastleN.S.W. 2308, Australia
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Since 1954, when Yang and Mills [7] presented their idea of isotopic gauge transformation, the method of introducing interactions into field theories by using general gauge invariance has been extensively studied.

A general formalism was presented by Utiyama [6]. Reference [6] also contains the first application of the formalism to the theory of gravitation. A more general approach to the Young-Mills formalism applied to general relativity was described by Kibble [3]. In a special case of interacting Dirac field the gauge invariance group can still be enlarged, leading to the possibility of describing short-range interactions together with gravitation and electromagnetism [5]. It is, therefore important to have a definite formulation of the common geometrical content of such theories.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 4 , June 1973 , pp. 482 - 487
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Hermann, R., Fourier Analysis on Groups and Partial Wave Analysis (W. A. Benjamin, 1968).Google Scholar
[2]Herman, R., Vector Bundles in Mathematical Physics (W. A. Benjamin, 1970).Google Scholar
[3]Kibble, T. W. B., ‘Lorentz invariance and the gravitational field’, J. Math. Phys. 2 (1961), 212–221.CrossRefGoogle Scholar
[4]Kobayashi, S. and Nomizu, K., Foundations of Differentialfi Geometry, Vol. I (Interscience Pub., 1963).Google Scholar
[5]Smrz, P., ‘Gauge invariance of the Dirac equation’, J. Aust. Math. Soc., 15 (1973), 117–122.CrossRefGoogle Scholar
[6]Utiyama, R., ‘Invariant theoretical interpretation of interaction,’ Phys. Rev. 101 (1956), 1597–1607.CrossRefGoogle Scholar
[7]Yang, C. N. and Mills, R. N., ‘Conservation of isotopic spin and isotopic gauge invariance’, Phys. Rev. 96 (1954), 191–195.CrossRefGoogle Scholar