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Einstein–Cartan Theory

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Geometrodynamics of Gauge Fields

Part of the book series: Mathematical Physics Studies ((MPST))

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Abstract

The difference between Einstein’s general relativity and its Cartan extension is analyzed classically as well as within the scenario of asymptotic safety of quantum gravity. In particular, we focus on the four-fermion interaction, which distinguishes the Einstein–Cartan theory from its Riemannian limit.

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Notes

  1. 1.

    Adding torsion squared terms (Daum & Reuter 2012, 2013) is not an unambiguous procedure, since the particular combination \( T^{\alpha }\wedge \;^{*}\!\Bigl (\,^{(1)}\!T_{\alpha } - 2\,^{(2)}\!T_{\alpha } -{1\over 2}\,^{(3)}\!T_{\alpha }\Bigr )\) of irreducible pieces is related to a nontopological boundary term derived from the dual CS term \(C_\mathrm{TT^*}:= \vartheta ^{\alpha }\wedge \,^* T_{\alpha }\). In the space of gravity theories, the term \(d C_\mathrm{TT^*}\) interrelates GR with its teleparallelism equivalent (Mielke 1992). Exactly, the above teleparallel “nucleus” leaves its traces in the controversies (Hecht et al. 1996; Ho & Nester 2011) about the well-posedness of the classical Cauchy problem and the particle content of the (broken) Poincaré gauge theory.

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  1. Departamento de Física, CBI Iztapalapa, Universidad Autónoma Metropolitana, Mexico City, México

    Eckehard W. Mielke

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Mielke, E.W. (2017). Einstein–Cartan Theory. In: Geometrodynamics of Gauge Fields. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-29734-7_5

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