2012/10/08 by Steffen Gielen
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Covariant transformation #Formalism (music) #General relativity #Gravitation #Gravitational field #Lorentz covariance #Lorentz transformation #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Spacetime #Spacetime symmetries #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1007/978-3-319-06761-2_70
published as Springer Proceedings in Physics 57 (2014) 497-503 · 8 pages, contribution to the proceedings of the conference "Relativity and Gravitation - 100 years after Einstein in Prague"; v2: added heading "References"
arxiv created 2012/10/08 · openalex publication_date 2014/01/01 · arxiv updated 2014/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In the Ashtekar-Barbero formulation of canonical general relativity based on an SU(2) connection, Lorentz covariance is a subtle issue which has been the focus of some debate. Here we present a Lorentz covariant formulation generalising the notion of a foliation of spacetime to a field of local observers which specify a time direction only locally. This field spontaneously breaks the local SO(3,1) symmetry down to a subgroup SO(3); we show that the apparent symmetry breaking to SO(3) is not in conflict with Lorentz covariance. We give a geometric picture of our construction as Cartan geometrodynamics and outline further applications of the formalism of local observers, motivating the idea that observer space, instead of spacetime, should serve as the fundamental arena for gravitational physics.