Poincaré Gauge Gravity Primer

Obukhov, Yuri N.

doi:10.1007/978-3-031-31520-6_3

Cited by 1 publication

(2 citation statements)

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“…An extension of GR, which is useful in describing fields with spin, is Einstein-Cartan (EC) theory [1][2][3][4][5][6][7][8][9][10][11]. In this case, the underlying geometry is Riemann-Cartan, which is characterized by both a curvature and a torsion tensor.…”

Section: Introductionmentioning

confidence: 99%

“…In many respects, local spacetime symmetries are similar to local gauge symmetries, where the latter are fundamental in the Standard Model (SM) in particle physics. This has led to considerable interest in EC theory formulated as a gauge theory, where Poincare symmetry is treated as a local gauge symmetry [3][4][5][6][7][8][9][10][11]. In this context, the fundamental spacetime symmetries consist of LLTs and local translations (LTs), and the vierbein becomes the gauge field for the LTs while the spin connection is the gauge field for the LLTs.…”

Section: Introductionmentioning

confidence: 99%

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Spontaneous and Explicit Spacetime Symmetry Breaking in Einstein–Cartan Theory with Background Fields

Bluhm,

Zhi

2023

Symmetry

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Explicit and spontaneous breaking of spacetime symmetry under diffeomorphisms, local translations, and local Lorentz transformations due to the presence of fixed background fields is examined in Einstein–Cartan theory. In particular, the roles of torsion and violation of local translation invariance are highlighted. The nature of the types of background fields that can arise and how they cause spacetime symmetry breaking is discussed. With explicit breaking, potential no-go results are known to exist, which if not evaded lead to inconsistencies between the Bianchi identities, Noether identities, and the equations of motion. These are examined in detail, and the effects of nondynamical backgrounds and explicit breaking on the energy–momentum tensor when torsion is present are discussed as well. Examples illustrating various features of both explicit and spontaneous breaking of local translations are presented and compared to the case of diffeomorphism breaking.

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