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The Rarita-Schwinger operator is the twisted Dirac operator restricted to 3/2-spinors. Rarita-Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare;…
We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group $R^l$. Under deformation by a torus action, a standard formula…
We solve for spectrum, obtain explicitly and study group properties of eigenfunctions of Dirac operator on the Riemann sphere $S^2$. The eigenvalues $\lambda$ are nonzero integers. The eigenfunctions are two-component spinors that belong to…
We review previous work of Alain Connes, and its extension by the author, on some conformal invariants obtained from the noncommutative residue on even dimensional compact manifolds without boundary. Inspired by recent work of Yong Wang, we…
Under suitable invertibility hypothesis, the spectrum of the Dirac operator on certain open spin Riemannian manifolds is discrete, and obeys a growth law depending qualitatively on the (in)finiteness of the volume.
In this short article, we non-perturbatively derive a recursive formula for the Green's function associated with finitely many point Dirac delta potentials in one dimension. We also extend this formula to the case for the Dirac delta…
It is shown that one can obtain canonically-defined dynamical equations for non-conservative mechanical systems by starting with a first variation functional, instead of an action functional, and finding their zeroes. The kernel of the…
We consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of m complex-valued half-densities over a connected compact n-dimensional manifold without boundary. The eigenvalues of the principal symbol are…
We study the inverse spectral problems of recovering Dirac-type functional-differential operator with two constant delays $a_1$ and $a_2$ not less than one-third of the interval. It has been proved that the operator can be recovered…
We prove an extension to R^n, endowed with a suitable metric, of the relation between the Einstein-Hilbert action and the Dirac operator which holds on closed spin manifolds. By means of complex powers, we first define the regularised…
We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the K\"all\'en-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are…
The spin 1 particle is treated in the presence of the Dirac magnetic monopole in the Minkowski and Lobachevsky spaces. Separating the variables in the frame of the matrix 10-component Duffin-Kemer-Petiau approach (wave equation) and making…
In this paper inverse problems for Dirac operator with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function and spectra are provided, which are generalizations of the well-known Weyl…
We study spectral action for Riemannian manifolds with boundary, and then generalize this to noncommutative spaces which are products of a Riemannian manifold times a finite space. We determine the boundary conditions consistent with the…
As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…
A Dirac operator is presented that will yield a 1+ summable regular even spectral triple for all noncommutative compact surfaces defined as subalgebras of the Toeplitz algebra. Connes' conditions for noncommutative spin geometries are…
On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of…
We derive an action for gravity in the framework of non-commutative geometry by using the Wodzicki residue. We prove that for a Dirac operator $D$ on an $n$ dimensional compact Riemannian manifold with $n\geq 4$, $n$ even, the Wodzicki…
Dirac equation for a charged spinor in electromagnetic field is written for special cases of spherically symmetric potentials. This facilitates the introduction of relativistic extensions of shape invariant potential classes. We obtain the…
The present article deals with differential equations with spectral parameter from the point of view of formal power series. The treatment does not make use of the notion of eigenvalue, but introduces a new idea: the spectral residue. The…