Different types of torsion and their effect on the dynamics of fields
arXiv:1907.02341 · doi:10.1140/epjp/i2018-12070-6
Abstract
One of the formalisms that introduces torsion conveniently 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 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.
arXiv commentThe final publication is available at Springer via https://doi.org/10.1140/epjp/i2018-12070-6
References in corpus (32)
- Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
- Physical Aspects of the Space-Time Torsion
- Accelerating universe from F(T) gravity
- Actions for Gravity, with Generalizations: A Review
- Nonsingular, big-bounce cosmology from spinor-torsion coupling
- Generalized Fierz identities
- Conformal transformations in classical gravitational theories and in cosmology
- Canonical Gravity with Fermions
- BF gravity and the Immirzi parameter
- Conformally invariant wave-equations and massless fields in de Sitter spacetime
- Weyl vs. Conformal
- gravity
- Exact solutions of Bianchi I spacetimes which admit Conformal Killing vectors
- A discussion on the most general torsion-gravity with electrodynamics for Dirac spinor matter fields
- Four-fermion interaction from torsion as dark energy
- Exact Static Cylindrical Solution to Conformal Weyl Gravity
- Metric-Torsional Conformal Gravity
- Torsion gravity with non-minimally coupled fermionic field: some cosmological models
- BF Description of Higher-Dimensional Gravity Theories
- Inflation by spin and torsion in Poincare gauge theory of gravity
- Representation-independent manipulations with Dirac matrices and spinors
- Continuity of the torsionless limit as a selection rule for gravity theories with torsion
- On the stability of self-accelerating Universe in modified gravity with dynamical torsion
- Conformal classes of asymptotically flat, static vacuum data
- BF gravity with Immirzi parameter and matter fields
- Conformal structures of static vacuum data
- Exact String-Like Solutions in Conformal Gravity
- Families of conformally related asymptotically flat, static vacuum data
- Conformal Gravity with Dirac Matter
- A Torsional Model of Leptons
- Conformal Gravity with Electrodynamics for Fermion Fields and their Symmetry Breaking Mechanism
- Conformal Standard Model
Cited by in corpus (9)
- Einstein manifolds with torsion and nonmetricity
- Non-zero torsion and late cosmology
- The Spin Tensor of Dark Matter and the Hubble Parameter Tension
- On the Mathematics of Coframe Formalism and Einstein-Cartan Theory -- A Brief Review
- Effect of spacetime geometry on neutrino oscillations
- Asymptotically AdS black hole with a conformally-coupled scalar field in the first-order formalism of gravity
- (In)equivalence of Metric-Affine and Metric Effective Field Theories
- Torsional four-fermion interaction and the Raychaudhuri equation
- Torsional modulation of atmospheric neutrino oscillation