Can nonlocal Dirac operators be topologically proper?

Can nonlocal Dirac operators be topologically proper ?

By examining the analyticity of a sequence of topologically-proper lattice Dirac operators, we show that they tend to a nonlocal Dirac operator. This implies that a nonlocal lattice Dirac operator can have exact zero modes satisfying the Atiyah-Singer index theorem, in gauge backgrounds with nonzero topological charge. PACS numbers: 11.15.Ha, 11.30.Rd, 11.30.Fs It is well known that all fundame...

Can nonlocal Dirac operators be topologically proper ? Ting

By examining the analyticity of a sequence of topologically-proper lattice Dirac operators, we show that they tend to a nonlocal Dirac operator. This implies that a nonlocal lattice Dirac operator can have exact zero modes satisfying the Atiyah-Singer index theorem, in gauge backgrounds with nonzero topological charge. PACS numbers: 11.15.Ha, 11.30.Rd, 11.30.Fs It is well known that all fundame...

Anomalies for Nonlocal Dirac Operators

The anomalies of a very general class of non local Dirac operators are computed using the ζ-function definition of the fermionic determinant and an asymmetric version of the Wigner transformation. For the axial anomaly all new terms introduced by the non locality can be brought to the standard minimal Bardeen’s form. Some extensions of the present techniques are also commented.

Dirac Operators

Perfect Refinement Operators can be Flexible

A (weakly) perfect ILP refinement operator was described in [1]. It’s main disadvantage however is that it is static and inflexible: for ensuring non-redundancy, some refinements of a hypothesis are disallowed in advance, regardless of the search heuristic which may recommend their immediate exploration. (Similar problems are faced by Progol and other complete and non-redundant systems). On the...