Related papers: Generalization of Chiral Symmetry for Tilted Dirac…
In presence of string solitons, index theorems for the generalised Dirac operators have to be revisited. We show that in supersymmetric configurations the fermionic operators decouple, so that there are no mixing effects between different…
We review the application of random matrix theory (RMT) to chiral symmetry in QCD. Starting from the general philosophy of RMT we introduce a chiral random matrix model with the global symmetries of QCD. Exact results are obtained for…
The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special "staggered" grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt…
In the planar limit, in the deconfined phase, the Euclidean Dirac operator has a spectral gap around zero. We show that functions of eigenvalues close to the spectral edge, which are independent of common rescalings and shifts gauge…
Motivated by the supersymmetric version of Dirac's theory, chiral models in field theory, and the quest of a geometric fundament for the Standard Model, we describe an approach to the differential geometry of vector bundles on…
We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with…
We report a numerical investigation of localization in the SU(2) model without diagonal disorder. At the band center, chiral symmetry plays an important role. Our results indicate that states at the band center are critical. States away…
We present a characterization, in terms of torsion-free generalized connections, for the integrability of various generalized structures (generalized almost complex structures, generalized almost hypercomplex structures, generalized almost…
Existence of a protected surface state described by a massless Dirac equation is a defining property of the topological insulator. Though this statement can be explicitly verified on an idealized flat surface, it remains to be addressed to…
We formulate Dirac fermions on a (1+1)-dimensional lattice based on a Hamiltonian formalism. The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around…
The topological non-triviality of insulating phases of matter is by now well understood through topological K-theory where the indices of the Dirac operators are assembled into topological classes. We consider in the context of the Kitaev…
A new class of lattice Dirac operators which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands…
The Wilson formulation of fermions in lattice gauge theory provides a unified description of the chiral anomalies in the standard model. The discrete Dirac operator diagonalizes into a series of two by two blocks. In each block the possible…
The geometrical underpinnings of a specific class of Dirac operators is discussed. It is demonstrated how this class of Dirac operators allow to relate various geometrical functionals like, for example, the Yang-Mills action and the…
It is shown that the main geometrical objects involved in all the symmetries or supersymmetries of the Dirac operators in curved manifolds of arbitrary dimensions are the Killing vectors and the Killing-Yano tensors of any ranks. The…
Assuming the spin-independence for confining force, we give a covariant quark representation of general composite meson systems with definite Lorentz transformation properties. For benefit of this representation we are able to deduce…
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…
We have generalized the solutions of the radial Dirac equation with a tensor potential under spin and pseudospin symmetry limits to exceptional orthogonal Hermite polynomials family. We have obtained new general rational potential models…
We propose a nonperturbative formulation of chiral gauge theories. The method involves a `pre-regulation' of the gauge fields, which may be implemented on a lattice, followed by a computation of the chiral fermion determinant in the form of…
With time reversal symmetry a Dirac operator has vanishing index and Chern number. We show that we can nevertheless define a nontrivial Z$_2$ index as well as a corresponding topological invariant given by gauge field, which implies that…