Noncommutative Geometry and Gauge Theories on Discrete Groups
arXiv:hep-th/9210098 · doi:10.1016/0393-0440(94)00009-S
Abstract
We build and investigate a pure gauge theory on arbitrary discrete groups. A systematic approach to the construction of the differential calculus is presented. We discuss the metric properties of the models and introduce the action functionals for unitary gauge theories. A detailed analysis of two simple models based on $\z_2$ and $\z_3$ follows. Finally we study the method of combining the discrete and continuous geometry.
LaTeX file, 23 pages, TPJU 7/92 (revised version)
References in corpus (4)
Cited by in corpus (18)
- Noncommutative Geometry of Finite Groups
- Differential calculus and gauge theory on finite sets
- Anomaly Cancellation Condition in Lattice Gauge Theory
- Gravity from Noncommutative Geometry
- Noncommutative Riemannian Geometry of the Alternating Group A_4
- Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories
- Discrete Differential Manifolds and Dynamics on Networks
- Differential Geometry of Group Lattices
- A Spinorial Formulation of the Maximum Clique Problem of a Graph
- BRST invariant Lagrangian of spontaneously broken gauge theories in noncommutative geometry
- Wilson Action of Lattice Gauge Fields with An Additional Term from Noncommutative Geometry
- Linear Connections on Graphs
- Quantizing Yang-Mills Theory on a 2-Point Space
- Dirac-Connes Operator on Discrete Abelian Groups and Lattices
- Classification of differentials and Cartan calculus on bicrossproducts
- BRST invariant formulation of spontaneously broken gauge theory in generalized differential geometry
- Gravity and Discrete Symmetry
- Difference Discrete Connection and Curvature on Cubic Lattice