Related papers: Geometric Constructions Underlying Relativistic De…
This article gives a geometric interpretation of the spin base formulation with local spin base invariance of spinors on a curved space-time and in particular of a central element, the global Dirac structure, in terms of principal and…
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…
Every Dirac spin structure on a world manifold is associated with a certain gravitational field, and is not preserved under general covariant transformations. We construct a composite spinor bundle such that any Dirac spin structure is its…
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 new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and…
We examine the construction of the spin angular momentum in systems with pseudoclassical Grassmann variables. In constrained systems there are many different algebraic forms for the dynamical variables that will all agree on the constraint…
In the framework of parallelism general relativity (PGR), the Dirac particle spin precession in the rotational gravitational field is studied. In terms of the equivalent tetrad of Kerr frame, we investigate the torsion axial-vector spin…
The gravitating matter is studied within the framework of the non-commutative geometry. The non-commutative Einstein-Hilbert action on the product of a four dimensional manifold with a discrete space gives the models of matter fields…
We construct the relativistic particle model without Grassmann variables which meets the following requirements. A) Canonical quantization of the model implies the Dirac equation. B) The variable which experiences {\it Zitterbewegung},…
Spinors have played an essential but enigmatic role in modern physics since their discovery. Now that quantum-gravitational theories have started to become available, the inclusion of a description of spin in the development is natural and…
We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic…
We define spin frames, with the aim of extending spin structures from the category of (pseudo-)Riemannian manifolds to the category of spin manifolds with a fixed signature on them, though with no selected metric structure. Because of this…
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 (arXiv:1508.07765v2…
The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily…
In gravitation theory, the realistic fermion matter is described by spinor bundles associated with the cotangent bundle of a world manifold $X$. In this case, the Dirac operator can be introduced. There is the 1:1 correspondence between…
In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define…
Motivated by the supersymmetric version of Dirac's theory, chiral models in field theory, and the quest of a geometric fundament for the Standard Model, we describe an approach to the differential geometry of vector bundles on…
We construct a new example of the spinning-particle model without Grassmann variables. The spin degrees of freedom are described on the base of an inner anti-de Sitter space. This produces both $\Gamma^\mu$ and $\Gamma^{\mu\nu}$\,-matrices…
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…
It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description…