We show how the standard domain wall action can be simply modified to allow arbitrarily exact chiral symmetry at finite fifth dimensional extent. We note that the method can be used for both quenched and dynamical calculations. We test the method using smooth and thermalized gauge field configurations. We also make comparisons of the performance (cost) of the domain wall operator for spectrosco...

We study the behavior of the spectrum of the Dirac operator on collapsing S1-bundles. Convergent eigenvalues will exist if and only if the spin structure is projectable.

In Clifford analysis, one studies spin-invariant differential operators on spaces of arbitrary dimension m. At the heart of the classical theory lies the well-known Dirac operator, which finds its origin in physics [5]: the Dirac equation describes the behaviour of electrons in the 4-dimensional spacetime. Our aim is to study generalizations of this operator, the so-called higher spin Dirac ope...

It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner-Nordström black hole background; in particular, there are no static solutions of the Dirac equation in such a background metric. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit aro...

We extend classical results of Kostant and al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted affine cubic Dirac operator. We prove in this setting an analogue of Vogan’s conjecture on infinitesimal characters of Harish–Chandra modules in terms of Dirac cohomology. For our calculations we use ...

Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates. PACS: 24.10.Jv, 21.60.Cs, 24.80.+y, 21.10.-k *E-mail address: [email protected] †E...

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations using the overlap Dirac operator. The bounds also apply to the Wilson Dirac operator in odd dimensions and are therefore relevant to domain wall fermions as well.

We explicitly determine the high-energy asymptotics for Weyl-Titchmarsh matrices associated with general Dirac-type operators on half-lines and on R. We also prove new local uniqueness results for Dirac-type operators in terms of exponentially small diierences of Weyl-Titchmarsh matrices. As concrete applications of the asymptotic high-energy expansion we derive a trace formula for Dirac operat...

For a Hamiltonian, proper and free action of a Lie group G on a Dirac manifold (M,L), with a regular moment map μ :M → g∗, the manifolds M/G, μ−1(0) and μ−1(0)/G all have natural induced Dirac structures. If (M,L) is an integrable Dirac structure, we show thatM/G is always integrable, but μ−1(0) and μ−1(0)/G may fail to be integrable, and we describe the obstructions to their integrability.