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Particles and Fields
Eur. Phys. J. C 17, 535-538
DOI 10.1007/s100520000481

Gauge symmetry as symmetry of matrix coordinates

A.H. Fatollahi1,2,3

1 Institute for Advanced Studies in Basic Sciences (IASBS), P.O. Box 45195-159, Zanjan, Iran
2 Institute for Studies in Theoretical Physics and Mathematics (IPM), P.O. Box 19395-5531, Tehran, Iran
3 High Energy Physics Division, Department of Physics, and Helsinki Institute of Physics, P.O. Box 9,
00014 University of Helsinki, Finland

Received: 16 June 2000 / Published online: 8 September 2000 - © Springer-Verlag 2000

We propose a new point of view on gauge theories, based on taking the action of symmetry transformations directly on the space coordinates. Via this approach the gauge fields are not introduced at the first step, and they can be interpreted as fluctuations around some classical solutions of the model. The new point of view is connected to the lattice formulation of gauge theories, and the parameter of the non-commutativity of the coordinates appears as the lattice spacing parameter. Through the statements concerning the continuum limit of lattice gauge theories, the suggestion arises that the non-commutative spaces are the natural ones to formulate gauge theories at strong coupling. Via this point of view, a close relation between the large-N limit of gauge theories and string theory can be made manifest.

Copyright Società Italiana di Fisica, Springer-Verlag 2000