Related papers: Euclidean Supergravity in Terms of Dirac Eigenvalu…

We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential…

We look at smooth manifolds equipped with a possibly singular Riemannian metric. We give sufficient conditions for the existence of scalar curvature measures and Dirac operators.

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 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…

In the standard treatment of particle oscillations the mass eigenstates are implicitly assumed to be scalars and, consequently, the spinorial form of neutrino wave functions is not included in the calculations. To analyze this additional…

Let $G/K$ be a simply connected spin compact inner irreducible symmetric space, endowed with the metric induced by the Killing form of $G$ sign-changed. We give a formula for the square of the first eigenvalue of the Dirac operator in terms…

We give a survey of results relating the restricted holonomy of a Riemannian spin manifold with lower bounds on the spectrum of its Dirac operator, giving a new proof of a result originally due to Kirchberg.

The advent of phenomenological quantum gravity has ushered us in the search for experimental tests of the deviations from general relativity predicted by quantum gravity or by string theories, and as a by--product of this quest the possible…

We study the higher spin Dirac operators on 3-dimensional manifolds and show that there exist two Laplace type operators for each associated bundle. Furthermore, we give lower bound estimations for the first eigenvalues of these Laplace…

Investigating properties of two-dimensional Dirac operators coupled to an electric and a magnetic field (perpendicular to the plane) requires in general unbounded (vector-) potentials. If the system has a certain symmetry, the fields can be…

We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator…

We show that the spectrum of the curl operator on a generic smoothly bounded domain in three-dimensional Euclidean space consists of simple eigenvalues. The main new ingredient in our proof is a formula for the variation of curl eigenvalues…

We carry the index theory for manifolds with boundary of B\"ar and Ballmann over to first order differential operators on metric graphs. This approach results in a short proof for the index of such operators. Then the self-adjoint…

We compute the spectrum of the Dirac operator on 3-dimensional Heisenberg manifolds. The behavior under collapse to the 2-torus is studied. Depending on the spin structure either all eigenvalues tend to $\pm\infty$ or there are eigenvalues…

We study the classical dynamics of a particle in Snyder spacetime, adopting the formalism of constrained Hamiltonian systems introduced by Dirac. We show that the motion of a particle in a scalar potential is deformed with respect to…

Inspired by problems arising in the geometrical treatment of Yang-Mills theories and Palatini's gravity, the covariant formulation of Hamiltonian dynamical systems as a Hamiltonian field theory of dimension $1+0$ on a manifold with boundary…

A Dirac spinor is coupled to topologically massive gravity and the D=3 dimensional action is reduced to D=2 dimensions with a metric that includes both the electromagnetic potential 1-form A and a dilaton scalar \phi. The dimensionnaly…

We consider the eigenvalues of the three-dimensional Weyl operator defined in terms of the (Euclidean) Ashtekar variables, and we study their dependence on the gravitational field. We notice that these eigenvalues can be used as…

The framework of the relativistic quantum mechanics on spatially flat FLRW space-times is considered for deriving the analytical solutions of the Dirac equation in different local charts of these manifolds. Systems of commuting conserved…

It is shown how a string living in a higher dimensional space can be approximated as a point particle with squared extrinsic curvature. We consider a generalized Howe-Tucker action for such a "rigid particle" and consider its classical…