Dirac fields in f(R)-gravity with torsion

TL;DR

This paper investigates how Dirac fields interact with f(R)-gravity incorporating torsion, revealing that the non-linear gravitational Lagrangian introduces a scalar field affecting fermion properties and conservation laws.

Contribution

It formulates conservation laws in f(R)-gravity with torsion, decomposes field equations to show the scalar field's role, and discusses implications for fermion energy positivity and duality.

Findings

Scalar field arises from non-linear gravity affecting Dirac fields

Conservation laws are consistent with matter equations

Fermion energy positivity and duality are analyzed

Abstract

We study f(R)-gravity with torsion in presence of Dirac massive fields. Using the Bianchi identities, we formulate the conservation laws of the theory and we check the consistency with the matter field equations. Further, we decompose the field equations in torsionless and torsional terms: we show that the non-linearity of the gravitational Lagrangian reduces to the presence of a scalar field that depends on the spinor field; this additional scalar field gives rise to an effective stress-energy tensor and plays the role of a scale factor modifying the normalization of Dirac fields. Problems for fermions regarding the positivity of energy and the particle-antiparticle duality are discussed.