Universität zu Köln

Baekler, Peter and Hehl, Friedrich W. ORCID: 0000-0003-2503-4744 (2011). Beyond Einstein-Cartan gravity: quadratic torsion and curvature invariants with even and odd parity including all boundary terms. Class. Quantum Gravity, 28 (21). BRISTOL: IOP PUBLISHING LTD. ISSN 1361-6382

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Abstract

Recently, gravitational gauge theories with torsion have been discussed by an increasing number of authors from a classical as well as from a quantum field theoretical point of view. The Einstein-Cartan(-Sciama-Kibble) Lagrangian has been enriched by the parity odd pseudoscalar curvature (Hojman, Mukku and Sayed) and by torsion square and curvature square pieces, likewise of even and odd parity. (i) We show that the inverse of the so-called Barbero-Immirzi parameter multiplying the pseudoscalar curvature, because of the topological Nieh-Yan form, can be appropriately discussed if torsion square pieces are included. (ii) The quadratic gauge Lagrangian with both parities, proposed by Obukhov et al and Baekler et al, emerges also in the framework of Diakonov et al. We establish the exact relations between both approaches by applying the topological Euler and Pontryagin forms in a Riemann-Cartan space expressed for the first time in terms of irreducible pieces of the curvature tensor. (iii) In a Riemann-Cartan spacetime, that is, in a spacetime with torsion, parity-violating terms can be brought into the gravitational Lagrangian in a straightforward and natural way. Accordingly, Riemann-Cartan spacetime is a natural habitat for chiral fermionic matter fields.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Baekler, Peter UNSPECIFIED UNSPECIFIED UNSPECIFIED Hehl, Friedrich W. UNSPECIFIED orcid.org/0000-0003-2503-4744 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-485540
DOI:	10.1088/0264-9381/28/21/215017
Journal or Publication Title:	Class. Quantum Gravity
Volume:	28
Number:	21
Date:	2011
Publisher:	IOP PUBLISHING LTD
Place of Publication:	BRISTOL
ISSN:	1361-6382
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language POINCARE GAUGE-THEORY; GENERAL-RELATIVITY; HAMILTONIAN ANALYSIS; BIANCHI IDENTITIES; NOETHER IDENTITIES; ENERGY-MOMENTUM; VIOLATION; SYMMETRIES; COMPUTER Multiple languages Astronomy & Astrophysics; Quantum Science & Technology; Physics, Multidisciplinary; Physics, Particles & Fields Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/48554