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Reassessing the foundations of metric-affine gravity
J François1,2,3, L Ravera4,5,6
1Department of Mathematics and Statistics, Masaryk University-MUNI, Kotlářská 267/2, Veveří, Brno, Czech Republic.
Metric-Affine Gravity (MAG) is reassessed using the Dressing Field Method. This approach streamlines MAG kinematics, revealing its reduction to Cartan-geometric kinematics, resolving gauge translation issues.
Area of Science:
- Theoretical Physics
- Gravitational Theories
- Differential Geometry
Background:
- Metric-Affine Gravity (MAG) presents challenges with gauge translations.
- Existing frameworks may not fully address the geometric nature of gauge theories.
- Systematic construction of gauge-invariant variables is crucial.
Purpose of the Study:
- To reassess foundational aspects of Metric-Affine Gravity (MAG).
- To apply the Dressing Field Method for building gauge-invariant field variables.
- To clarify the geometric status of gauge translations within MAG.
Main Methods:
- Utilizing the Dressing Field Method to systematically construct gauge-invariant field variables.
- Recalling Cartan geometry as the mathematical foundation for gauge theories of gravity.
- Analyzing the kinematics of MAG through the lens of the Dressing Field Method.
Main Results:
- The Dressing Field Method provides a streamlined approach to MAG kinematics.
- MAG kinematics is shown to reduce to a Cartan-geometric kinematics.
- The framework of Cartan geometry inherently resolves issues with gauge translations.
Conclusions:
- The Dressing Field Method offers a technically streamlined pathway to MAG.
- Metric-Affine Gravity's kinematics is fundamentally linked to Cartan geometry.
- Cartan geometry provides a robust foundation for understanding gauge translations in gravity.
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