Radiation condition for Dirac operators

Dirac Operators

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.

p-Dirac Operators

We introduce non-linear Dirac operators in R associated to the p-harmonic equation and we extend to other contexts including spin manifolds and the sphere.

Higher spin Dirac operators

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...

Natural Equivariant Dirac Operators

We introduce a new class of natural, explicitly defined, transversally elliptic differential operators over manifolds with compact group actions. Under certain assumptions, the symbols of these operators generate all the possible values of the equivariant index. We also show that the components of the representation-valued equivariant index coincide with those of an elliptic operator constructe...