Gauge networks in noncommutative geometry

JOURNAL OF GEOMETRY AND PHYSICS

卷:75

Article

Marcolli, Matilde¹  van Suijlekom, Walter D.² 

[1] CALTECH, Div Phys Math & Astron, Pasadena, CA 91125 USA

[2] Radboud Univ Nijmegen, Inst Math Astrophys & Particle Phys, NL-6525 AJ Nijmegen, Netherlands

关键词: Noncommutative geometry;    Spin networks;    Lattice gauge theory;   

DOI  :  10.1016/j.geomphys.2013.09.002

来源: Elsevier

【 摘 要 】

We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo equivalence) in the category of finite spectral triples is studied; gauge networks appear as an orthonormal basis in a corresponding Hilbert space. We give many examples of gauge networks, also beyond the well-known spin network examples. We find a Hamiltonian operator on this Hilbert space, inducing a time evolution on the C*-algebra of gauge network correspondences. Given a representation in the category of spectral triples of a quiver embedded in a spin manifold, we define a discretized Dirac operator on the quiver. We compute the spectral action of this Dirac operator on a four-dimensional lattice, and find that it reduces to the Wilson action for lattice gauge theories and a Higgs field lattice system. As such, in the continuum limit it reduces to the Yang-Mills-Higgs system. For the three-dimensional case, we relate the spectral action functional to the Kogut-Susskind Hamiltonian. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free