Related papers: Isospectral deformations of the Dirac operator

Normality of the Dirac operator is shown to be necessary for chiral properties. From the global chiral Ward identity, which in the continuum limit gives the index theorem, a sum rule results which constrains the spectrum. The…

In this paper we analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric…

In this thesis, we show the existence of a sequence of differential operators starting with with the Dirac operator in k Clifford variables, $D=(D_1,..., D_k)$, where $D_i=\sum_j e_j\cdot \partial_{ij}: C^\infty((\R^n)^k,\S)\to…

The magnetic Dirac operator describes the relativistic motion of a charged particle in a magnetic field. Although this operator got a lot of attention in physics many of its fundamental mathematical properties remain unexplored and this…

We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the spectrum…

A Dirac operator D on quantized irreducible generalized flag manifolds is defined. This yields a Hilbert space realization of the covariant first-order differential calculi constructed by I. Heckenberger and S. Kolb. All differentials…

Consider the Schr\"{o}dinger operator $H = -\Delta + V$, where the potential $V$ is real, $\mathbb{Z}^2$-periodic, and additionally invariant under the symmetry group of the square. We show that, under typical small linear deformations of…

Let $(M^{n}, g)$ denote a Riemannian spin manifold of dimension $n$ with Dirac operator $D$ induced from the Levi-Cevita connection acing on the spinor bundle, $S$ ($D$ is also called the Atiyah-Singer Operator). Let $c: Cl(TM^{n})…

In this paper we present a summarizing description of the connection between Dirac operators on conformally flat manifolds and automorphic forms based on a series of joint work with John Ryan over the last fifteen years. We also outline…

Starting with Lagrangians, which turn out to be degenerate, the Hamiltonian operators for integrable systems can be constructed using Dirac's theory of constraints. We illustrate this by giving a systematic discussion of the first…

Dirac's contour representation is extended to parabose and parafermi systems by use of deformed algebra techniques. In this analytic representation the action of the paraparticle annihilation operator is equivalent to a deformed…

We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact…

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…

We study Dirac operators acting on sections of a Clifford module ${\cal E}$\ over a Riemannian manifold $M$. We prove the intrinsic decomposition formula for their square, which is the generalisation of the well-known formula due to…

We introduce a family of metric-deformed Heisenberg algebras $M_1$ and $M_2$, where the commutation relations are expressed directly in terms of the components of a diagonal Lorentzian metric. We show that these algebras unify several known…

Complete spectra of the staggered Dirac operator $\Dirac$ are determined in four-dimensional $SU(2)$ gauge fields with and without dynamical fermions. An attempt is made to relate the performance of multigrid and conjugate gradient…

In this study, we obtain a spinorial Gauss formula for a lightlike hypersurface in Lorentzian manifold with 4-dimension. Then, we take into account the changes caused by degenerate metric on hypersurface and investigate Dirac operator for…

The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact…

Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…

The k-Dirac operator is a differential operator which is natural to geometric structure of a parabolic type. We will give a set of initial conditions for this operator. In the proof of the claim we will need to adapt some parts from the…