Related papers: A modified gravity model coupled to a Dirac field …
We take a Dirac field non-minimally coupled to the gravitational field within the framework of the Poincar\'e gauge theory of gravity with torsion and curvature. We study the subcase of "weak" gravity, that is, the gravitational Lagrangian…
We show that the exterior algebra bundle over a curved spacetime can be used as framework in which both the Dirac and the Einstein equations can be obtained. These equations and their coupling follow from the variational principle applied…
Gauge fields associated to the Dirac matrix algebra used with the standard quadratic gauge field Lagrangian lead to an extended gravitational Lagrangian which includes the Einstein-Hilbert one, plus quadratic, cosmological constant and…
Minimal coupling of a Dirac field to gravity with the most general non-propagating torsion is considered in (1+2)-dimensions. The field equations are obtained from a lagrangian by a variational principle. The space-time torsion is…
The main fundamental principles characterizing the vacuum field structure are formulated and the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The work is…
We suggest model equations, which, from some point of view, describe local interaction of three physical fields: a field of matter, an electromagnetic field and a gravitational field. A base of the model is a field of matter described by…
Here we consider a metric-affine theory of gravity in which the gravitational Lagrangian is the scalar curvature. The matter action is allowed to depend also on the torsion and the nonmetricity, which are considered as the field variables…
We apply the covariant analytic mechanics with the differential forms to the Dirac field and the gravity with the Dirac field. The covariant analytic mechanics treats space and time on an equal footing regarding the differential forms as…
In the present paper we consider a theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, both with their own coupling constant. In particular, we discuss the couplings to Dirac fields and…
We propose a cosmological model in the framework of the Poincar\'e gauge theory of gravity (PG). The gravitational Lagrangian is quadratic in curvature and torsion. In our specific model, the Lagrangian contains (i) the curvature scalar $R$…
A Lagrangian theory giving rise to a version of the Dirac-Kahler equations on curved backgrounds is considered. The principal pieces are the general fields which have values in the algebra of the Dirac matrices and satisfy a Dirac-type…
GR and other metric theories of gravity are formulated with an arbitrary auxiliary curved background in a Lagrangian formalism. A new sketch of how to include spinor fields is included. Conserved quantities are obtained using Noether's…
We clarify the structure obtained in H\'elein and Vey's proposition for a variational principle for the Einstein-Cartan gravitation formulated on a frame bundle starting from a structure-less differentiable 10-manifold. The obtained…
A Poincar\'{e} gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that…
We discuss the most general form of Dirac equation in the non$-$Riemannian spacetimes containing curvature, torsion and non$-$metricity. It includes all bases of the Clifford algebra $cl(1,3)$ within the spinor connection. We adopt two…
We discuss the Dirac quantization of two dimensional gravity with bosonic matter fields. After defining the extended Hamiltonian it is possible to fix the gauge completely. The commutators can all be obtained in closed form; nevertheless,…
Stabilizing, by deformation, the algebra of relativistic quantum mechanics a non-commutative space-time geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a…
We study reparametrization-invariant systems, mainly the relativistic particle and its D-dimensional extended object generalization--d-brane. The corresponding matter Lagrangians naturally contain background interactions, like…
The interaction of matter with gravity in two dimensional spacetimes can be supplemented with a geometrical force analogous to a Lorentz force produced on a surface by a constant perpendicular magnetic field. In the special case of constant…