The overlap Dirac operator, derived from the overlap formalism for the special case of vector gauge theories, is a way to realize exact chiral symmetry on the lattice. Exact chiral symmetry on the lattice does come at a price – numerical implementation of the overlap Dirac operator is significantly more expensive than Wilson or staggered operator. In spite of this numerical hurdle, we already h...

Transformation properties of Dirac equation correspond to Spin(3,1) representation of Lorentz group SO(3,1), but group GL(4,R) of general relativity does not accept a similar construction with Dirac spinors. On the other hand, it is possible to look for representation of GL(4,R) in some bigger space, there Dirac spinors are formally situated as some " subsystem. " In the paper is described cons...

Manifolds with fibered hyperbolic cusp metrics include hyperbolic manifolds with cusps and locally symmetric spaces of Q-rank one. We extend Vaillant’s treatment of Dirac-type operators associated to these metrics by weaking the hypotheses on the boundary families through the use of Fredholm perturbations as in the family index theorem of Melrose and Piazza and by treating the index of families...

We show how the standard domain wall action can be simply modified to allow arbitrarily exact chiral symmetry at finite fifth dimensional extent Ls. 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 spectro...

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 general theory of external symmetry transformations associated to the usual isometries is presented, pointing out that these leave the standard Dirac equation inva...

That a Majorana neutrino theory is different from a Dirac neutrino theory (even in the zero mass limit) is proved in two sentences. Fermion Statistics For the reactions (Dirac) e + e − → ν ¯ ν and (Majorana) e + e − → νν wherein the two final particles are presumed to have opposite helicity, in the Dirac case the neutrino and anti-neutrino are different particles so that Ψ Dirac (p 1 , λ 1 ; ¯ ...