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Open AccessArticle

Scale Transformations in Metric-Affine Geometry

by Damianos Iosifidis 1 and Tomi Koivisto 2,3,4,5,*
Institute of Theoretical Physics, Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden
Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
National Institute of Chemical Physics and Biophysics, Rävala pst. 10, 10143 Tallinn, Estonia
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;
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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