Vacuum Solutions of Classical Gravity on Cyclic Groups from Noncommutative Geometry
Abstract
Based on the observation that the moduli of a link variable on a cyclic group modify Connes' distance on this group, we construct several action functionals for this link variable within the framework of noncommutative geometry. After solving the equations of motion, we find that one type of action gives nontrivial vacuum solution for gravity on this cyclic group in a broad range of coupling constants and that such a solution can be expressed with Chebyshev's polynomials.
The project supported by Climb-Up (Pan Deng) Project of Department of Science and Technology of China, National Natural Science Foundation of China and Doctoral Programme Foundation of Institution of Higher Education of China- Publication:
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Communications in Theoretical Physics
- Pub Date:
- January 2002
- DOI:
- arXiv:
- arXiv:gr-qc/0102028
- Bibcode:
- 2002CoTPh..37...11D
- Keywords:
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- General Relativity and Quantum Cosmology;
- High Energy Physics - Lattice;
- High Energy Physics - Theory
- E-Print:
- Latex 7 pages