Related papers: Dimensional Reduction of Dirac Operator
Recent lattice results on Dirac low-mode removed $J=1,2$ mesons and $J=\frac{1}{2}$ baryons reveal the appearance of a new $SU(4)$ symmetry of confinement. Here the degeneracy of all $J=2$ iso-vector states within an irreducible…
We have obtained the supersymmetric extension of spectral triple which specify a noncommutative geometry(NCG). We assume that the functional space H constitutes of wave functions of matter fields and their superpartners included in the…
We describe the structure of the vacuum states of quiver gauge theories obtained via dimensional reduction over homogeneous spaces, in the explicit example of SU(3)-equivariant dimensional reduction of Yang-Mills-Dirac theory on manifolds…
A new approach to the study of spectral asymmetry for systems of partial differential equations (PDEs) on closed manifolds was proposed in a recent series of papers by the first author and collaborator. They showed that information on…
The aim of this paper is to investigate the separability of a spin-1/2 spinor field in a five-dimensional rotating, charged black hole constructed by Cvetic and Youm in string theory, in the case when three U(1) charges are set equal. This…
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.…
The paper analyses the decay of any zero modes that might exist for a massless Dirac operator $H:= \ba \cdot (1/i) \bgrad + Q, $ where $Q$ is $4 \times 4$-matrix-valued and of order $O(|\x|^{-1})$ at infinity. The approach is based on…
We consider Dirac-type operators on manifolds with boundary, and set out to determine all local smooth boundary conditions that give rise to (strongly) regular self-adjoint operators. By combining the general theory of boundary value…
We study the spectrum of the Dirac operator $D$ on pseudo-Riemannian spin manifolds of signature $(p,q)$, considered as an unbounded operator in the Hilbert space $L^2_\xi(S)$. The definition of $L^2_\xi(S)$ involves the choice of a…
A generic-curved spacetime Dirac-like equation in 3D is constructed. It has, owing to the $\bar{SL}(n,R)$ group deunitarizing automorphism, a physically correct unitarity and flat spacetime particle properties. The construction is achieved…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncom- mutative space where the noncommutativity is induced by a shift of the dynamical variables with generators of SL(2;R) in a unitary irreducible…
A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal…
After a brief historical survey that emphasizes the role of the algebra obeyed by the Dirac operator, we examine an algebraic Dirac operator associated with Lie algebras and Lie algebra cosets. For symmetric cosets, its ``massless''…
Spectral triples over noncommutative principal $\T^n$-bundles are studied, extending recent results about the noncommutative geometry of principal U(1)-bundles. We relate the noncommutative geometry of the total space of the bundle with the…
The group SU(3) is parameterized in terms of generalized ``Euler angles''. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is…
The Dirac equation in the external Coulomb field is proved to possess the symmetry determined by the 31 operators, which form the 31-dimensional algebra. Two different fermionic realizations of the SO(1,3) algebra of the Lorentz group are…
A generalization of the Dirac field equation in three-dimensional Minkowski space-time to the case of the $\bar{SL}(3,R)$ $\subset$ $\bar{SA}(3,R)$ symmetry is considered. Constraints that ensure a correct physical interpretation of the…
Properties of the Cauchy-Riemann-Fueter equation for maps between quaternionic manifolds are studied. Spaces of solutions in case of maps from a K3-surface to the cotangent bundle of a complex projective space are computed. A relationship…
Dirac fermions in the fundamental representation of SU(N) live on the surface of a cylinder embedded in $R^3$ and interact with a three dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the…