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U(1) gauge theory over discrete space-time and phase transitions

L. Z. Hu
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Abstract

We first apply Connes' noncommutative geometry to a finite point space. The explicit form of the action functional of U(1) gauge field on this n-point space is obtained. We then consider the case when the n-point space is replaced by {space-time}\times{n-point space}. This action is shown to relate the Hamiltonian of the continuous-spin formulation of the Potts model. We argue that U(1) gauge theory on the discrete space-time determines the geometric origin of a class of phase transitions.

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L. Z. Hu. 2000-01-22. U(1) gauge theory over discrete space-time and phase transitions. https://arxiv.org/abs/hep-th/0001148

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