Relating Noncommutative SO(2,3)★ Gravity to the Lorentz-Violating Standard-Model Extension
Abstract
:1. Introduction
2. Noncommutative SO(2,3) Gravity
3. Gravitational Sector of the Lorentz-Violating Standard-Model Extension
3.1. Covariant Match
3.2. Linearized Lorentz-Violating Standard-Model Extension
4. Connecting NC SO(3,2) Gravity to the SME
5. Conclusions, Prospects for Further Work
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Geometric Quantities to 2nd Order in the Metric Perturbation
- Metric:
- Vierbein:
- Note again that the expressions for the vierbein quantities cannot be related to each other simply by raising and lowering indices: , etc. Note also that the index placement in the definition of e is important: .
- Connection coefficients:
- Derivative compatibility:
- Riemann tensor:
- Ricci tensor:
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u | Weight C | Geometric Quantity L |
---|---|---|
1 | ||
2 | ||
3 | ||
4 | ) | |
5 | ||
6 |
SME Coefficients | Young Projection |
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Bailey, Q.G.; Lane, C.D. Relating Noncommutative SO(2,3)★ Gravity to the Lorentz-Violating Standard-Model Extension. Symmetry 2018, 10, 480. https://doi.org/10.3390/sym10100480
Bailey QG, Lane CD. Relating Noncommutative SO(2,3)★ Gravity to the Lorentz-Violating Standard-Model Extension. Symmetry. 2018; 10(10):480. https://doi.org/10.3390/sym10100480
Chicago/Turabian StyleBailey, Quentin G., and Charles D. Lane. 2018. "Relating Noncommutative SO(2,3)★ Gravity to the Lorentz-Violating Standard-Model Extension" Symmetry 10, no. 10: 480. https://doi.org/10.3390/sym10100480