2014/03/17 by Manuel Hohmann, Hohmann, Manuel
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1403.4005
43 pages, 2 figures; invited contribution to "Mathematical Structures of the Universe", Copernicus Center Press, Krakow, 2014, ISBN 978-83-7886-107-2; minor corrections to match published version
openalex publication_date 2014/03/17 · arxiv created 2014/09/11 · arxiv updated 2014/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian metric. Approaches to quantum gravity, however, hint towards a breaking of these symmetries and the possible existence of more general, non-tensorial geometric structures. Possible implications of these approaches are non-tensorial transformation laws between different observers and an observer-dependent notion of geometry. In this work we review two different frameworks for observer dependent geometries, which may provide hints towards a quantization of gravity and possible explanations for so far unexplained phenomena: Finsler spacetimes and Cartan geometry on observer space. We discuss their definitions, properties and applications to observers, field theories and gravity.