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2013•International Journal of Modern Physics AOpen access

GAUGE THEORY ON A SPACE WITH LINEAR LIE TYPE FUZZINESS

Mohammad Khorrami, Amir H. Fatollahi, Ahmad Shariati

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Abstract

The U(1) gauge theory on a space with Lie type noncommutativity is constructed. The construction is based on the group of translations in Fourier space, which in contrast to space itself is commutative. In analogy with lattice gauge theory, the object playing the role of flux of field strength per plaquette, as well as the action, is constructed. It is observed that the theory, in comparison with ordinary U(1) gauge theory, has an extra gauge field component. This phenomena is reminiscent of similar ones in formulation of SU (N) gauge theory in space with canonical noncommutativity, and also appearance of gauge field component in discrete direction of Connes' construction of the Standard Model.

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The U(1) gauge theory on a space with Lie type noncommutativity is constructed. The construction is based on the group of translations in Fourier space, which in contrast to space itself is commutative. In analogy with lattice gauge theory, the object playing the role of flux of field strength per plaquette, as well as the action, is constructed. It is observed that the theory, in comparison with ordinary U(1) gauge theory, has an extra gauge field component. This phenomena is reminiscent of similar ones in formulation of SU (N) gauge theory in space with canonical noncommutativity, and also appearance of gauge field component in discrete direction of Connes' construction of the Standard Model.

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Available abstract

The U(1) gauge theory on a space with Lie type noncommutativity is constructed. The construction is based on the group of translations in Fourier space, which in contrast to space itself is commutative. In analogy with lattice gauge theory, the object playing the role of flux of field strength per plaquette, as well as the action, is constructed. It is observed that the theory, in comparison with ordinary U(1) gauge theory, has an extra gauge field component. This phenomena is reminiscent of similar ones in formulation of SU (N) gauge theory in space with canonical noncommutativity, and also appearance of gauge field component in discrete direction of Connes' construction of the Standard Model.

Key concepts: Hamiltonian lattice gauge theory, Introduction to gauge theory, Lattice gauge theory, Quantum gauge theory, Gauge anomaly, Gauge theory, Supersymmetric gauge theory, BRST quantization

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