Related papers: The tensor Dirac equation in Riemannian space

Compatibility of symmetric quantization of the Dirac equation in a curved space with general covariance gives a special representation of the spin connections in which their dot product with the Dirac gamma matrices becomes equal to the…

By analysing the work of Campolattaro we argue that the second Seiberg-Witten equation over the Spin^c_4 manifold, i.e., F^+_{ij}=< M,S_ij M >, is the generalization of the Campolattaro's description of the electromagnetic field tensor…

In this article, we derive an integral formula involving the tensor $D_{ijk}$ for compact Einstein-type manifolds with constant scalar curvature. As an application, we classify three-dimensional compact Einstein-type manifolds satisfying…

We explicitly compute the spectral metric, torsion and Einstein tensors for a nontrivial spectral triple on a noncommutative torus, with the Dirac operator related to the fully equivariant Dirac by a partial conformal rescaling (as…

The metric tensor field equations for the general quadratic curvature gravity in four spacetime dimensions are derived by making use of the algebra of the exterior forms defined on pseudo-Riemannian manifolds and the identities satisfied by…

We generalize the well-known lower estimates for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold proved by Th. Friedrich (1980) and O. Hijazi (1986, 1992). The special solutions of the Einstein-Dirac…

We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally…

The authors of that work [Phys. Rev. D 88, 084014 (2013)], arXiv:1308.4552, derive quantum-mechanical equations valid for the covariant Dirac equation by restricting the choice of the tetrad field through the use of the "Schwinger gauge".…

We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c manifolds; and conversely, in the presence…

The work is devoted to the generalization of the Dirac equation for a flat locally anisotropic, i.e., Finslerian space-time. At first we reproduce the corresponding metric and a group of the generalized Lorentz transformations, which has…

There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue…

A Clifford Space is counted to be a tempting approach to unify both micro-physics and macro-physics simultaneously. Such a tendency may be found in the realm of replacing vectors with poly-vectors. Accordingly, the problem of motion becomes…

We investigate the structure of the Klein-Gordon-Fock equation symmetry algebra on pseudo-Riemannian manifolds with motions in the presence of an external electromagnetic field. We show that in the case of an invariant electromagnetic field…

We reexamine the minimal coupling procedure in the Hestenes' geometric algebra formulation of the Dirac equation, where spinors are identified with the even elements of the real Clifford algebra of spacetime. This point of view, as we…

We present various generalizations of the Dirac formalism. The different-parity solutions of the Weinberg's 2(2J+1)-component equations are found. On this basis, generalizations of the Bargmann-Wigner (BW) formalism are proposed. Relations…

Transformation properties of Dirac equation correspond to Spin(3,1) representation of Lorentz group SO(3,1), but group GL(4,R) of general relativity does not accept a similar construction with Dirac spinors. On the other hand, it is…

In flat spacetime, the Dirac equation is the "square root" of the Klein-Gordon equation in the sense that by applying the square of the Dirac operator to the Dirac spinor, one recovers the Klein-Gordon equation duplicated for each component…

In the framework of spacetime with torsion and without curvature, the Dirac particle spin precession in the rotational system is studied. We write out the equivalent tetrad of rotating frame, in the polar coordinate system, through…

The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…

The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential…