A modified gravity model coupled to a Dirac field in 2D spacetimes with quadratic nonmetricity and curvature

Abstract

After summarizing basic concepts for the exterior algebra we firstly discuss the gauge structure of the bundle over base manifold for deciding the form of the gravitational sector of the total Lagrangian in any dimensions. Then we couple minimally a Dirac spinor field to our gravitational Lagrangian 2-form which is quadratic in the nonmetricity and both linear and quadratic in the curvature in two dimensions. Subsequently we obtain field equations by varying the total Lagrangian with respect to the independent variables. Finally we find some classes of solutions of the vacuum theory and then a solution of the Dirac equation in a specific background and analyse them.

arXiv commentAccepted for publication in IJGMMP

References in corpus (16)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Dilaton Gravity in Two Dimensions
• Lagrange formulation of the symmetric teleparallel gravity
• Observable traces of non-metricity: new constraints on metric-affine gravity
• Instabilities in Metric-Affine Theories of Gravity
• Metric-affine gauge theory of gravity II. Exact solutions
• Black Holes with Weyl Charge and Non-Riemannian Waves
• The Cauchy problem of f(R) gravity
• Gauge Approach to The Symmetric Teleparallel Gravity
• On an integrable geometrical foundation of gravity
• Scalars, Vectors and Tensors from Metric-Affine Gravity
• Possible effects of spacetime non-metricity on neutrino oscillations
• The Quadratic Symmetric Teleparallel Gravity in Two-Dimensions
• Projective symmetries and induced electromagnetism in metric-affine gravity
• The Quantized $O(1,2)/O(2)\times Z_2$ Sigma Model Has No Continuum Limit in Four Dimensions. II. Lattice Simulation
• The Symmetric Teleparallel Gravity

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• The non-minimally coupled symmetric teleparallel gravity with electromagnetic field
• Weyl-Lorentz-U(1)-invariant symmetric teleparallel gravity in three dimensions