Different types of torsion and their effect on the dynamics of fields
S. N. Bose National Centre for Basic Sciences, Block - JD, Sector - III, 700106, Kolkata, India
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Accepted: 22 May 2018
Published online: 28 June 2018
One of the formalisms that conveniently introduces torsion in gravity is the vierbein-Einstein-Palatini (VEP) formalism. The independent variables are the vierbein (tetrads) and the components of the spin connection. The latter can be eliminated in favor of the tetrads using the equations of motion in the absence of fermions; otherwise there is an effect of torsion on the dynamics of fields. We find that the conformal transformation of off-shell spin connection is not uniquely determined unless additional assumptions are made. One possibility gives rise to the Nieh-Yan theory, another one to conformally invariant torsion; a one-parameter family of conformal transformations interpolates between the two. We also find that for dynamically generated torsion the spin connection does not have well-defined conformal properties. In particular, it affects fermions and the non-minimally coupled conformal scalar field.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018