Gauge gravitation theory
In
Gauge gravitation theory should not be confused with the similarly named gauge theory gravity, which is a formulation of (classical) gravitation in the language of geometric algebra. Nor should it be confused with Kaluza–Klein theory, where the gauge fields are used to describe particle fields, but not gravity itself.
Overview
The first gauge model of gravity was suggested by Ryoyu Utiyama (1916–1990) in 1956
In order to overcome this drawback, representing
Difficulties of constructing gauge gravitation theory by analogy with the Yang–Mills one result from the gauge transformations in these theories belonging to different classes. In the case of internal symmetries, the gauge transformations are just vertical automorphisms of a principal bundle leaving its base fixed. On the other hand,
In terms of gauge theory on natural bundles, gauge fields are linear connections on a world manifold , defined as principal connections on the linear frame bundle , and a metric (tetrad) gravitational field plays the role of a Higgs field responsible for spontaneous symmetry breaking of general covariant transformations.[7]
Spontaneous symmetry breaking is a quantum effect when the vacuum is not invariant under the transformation group. In classical gauge theory, spontaneous symmetry breaking occurs if the
The idea of the pseudo-Riemannian metric as a Higgs field appeared while constructing non-linear (induced) representations of the general linear group GL(4, R), of which the Lorentz group is a Cartan subgroup.[9] The geometric equivalence principle postulating the existence of a reference frame in which Lorentz invariants are defined on the whole world manifold is the theoretical justification for the reduction of the structure group GL(4, R) of the linear frame bundle FX to the Lorentz group. Then the very definition of a pseudo-Riemannian metric on a manifold as a global section of the quotient bundle FX / O(1, 3) → X leads to its physical interpretation as a Higgs field. The physical reason for world symmetry breaking is the existence of Dirac fermion matter, whose symmetry group is the universal two-sheeted covering SL(2, C) of the restricted Lorentz group, SO+(1, 3).[10]
See also
References
- ^ Utiyama, R. (1956). "Invariant theoretical interpretation of interaction". Physical Review. 101: 1597. .
- ^
Blagojević, Milutin; Hehl, Friedrich W. (2013). Gauge Theories of Gravitation: A Reader with Commentaries. World Scientific. ISBN 978-184-8167-26-1.
- ^ Hehl, F.; McCrea, J.; Mielke, E.; Ne'eman, Y. (1995). "Metric-affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilaton invariance". Physics Reports. 258: 1. .
- ^ Malyshev, C. (2000). "The dislocation stress functions from the double curl T(3)-gauge equations: Linearity and look beyond". Annals of Physics. 286: 249. .
- ^ Blagojević, M. (2002). Gravitation and Gauge Symmetries. Bristol, UK: IOP Publishing.
- ^ Kolář, I.; Michor, P.W.; Slovák, J. (1993). Natural Operations in Differential Geometry. Berlin & Heidelberg: Springer-Verlag.
- ^ .
- ^ Nikolova, L.; Rizov, V. (1984). "Geometrical approach to the reduction of gauge theories with spontaneous broken symmetries". Reports on Mathematical Physics. 20: 287. .
- ^ Leclerc, M. (2006). "The Higgs sector of gravitational gauge theories". Annals of Physics. 321: 708. .
- ^ Sardanashvily, G.; Zakharov, O. (1992). Gauge Gravitation Theory. Singapore: World Scientific.
Bibliography
- Kirsch, I. (2005). "A Higgs mechanism for gravity". Phys. Rev. D. 72: 024001. arXiv:hep-th/0503024.
- arXiv:1110.1176.
- Obukhov, Yu. (2006). "Poincaré gauge gravity: Selected topics". Int. J. Geom. Methods Mod. Phys. 3: 95–138. arXiv:gr-qc/0601090.