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Open AccessArticle

Scale Transformations in Metric-Affine Geometry

by Damianos Iosifidis 1 and Tomi Koivisto 2,3,4,5,*
1
Institute of Theoretical Physics, Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
2
Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden
3
Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
4
National Institute of Chemical Physics and Biophysics, Rävala pst. 10, 10143 Tallinn, Estonia
5
Helsinki Institute of Physics and Department of Physical Sciences, Helsinki University, P.O. Box 64, FIN-00014 Helsinki, Finland
*
Author to whom correspondence should be addressed.
Universe 2019, 5(3), 82; https://doi.org/10.3390/universe5030082
Received: 17 January 2019 / Revised: 5 March 2019 / Accepted: 11 March 2019 / Published: 15 March 2019
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformation of the connection, a rescaling of the orthonormal frame, and a combination of the two. The most general second order quadratic metric-affine action, including the parity-violating terms, is constructed in each of the three cases. The results can be straightforwardly generalised by including higher derivatives, and implemented in the general metric-affine, teleparallel, and symmetric teleparallel geometries. View Full-Text
Keywords: scale invariance; Palatini formalism; metric affine gauge theory of gravity scale invariance; Palatini formalism; metric affine gauge theory of gravity
MDPI and ACS Style

Iosifidis, D.; Koivisto, T. Scale Transformations in Metric-Affine Geometry. Universe 2019, 5, 82.

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