MPEJ Volume 4, No.4, 16pp
Received: Apr 3, 1998, Revised: Aug 21, 1998, Accepted: Sep 14, 1998

Bernard Helffer, Heinz Siedentop
Form Perturbations of the Second Quantized Dirac Field

ABSTRACT.  We give a criterion on when a form perturbation of the free Dirac
operator defines a form perturbation of the second quantized free Dirac field.
Moreover, we show that the potentials allowing this quantization are regular
in the sense of Klaus and Scharf. Furthermore we prove that only non-local
potentials allow for this construction in three dimensions. In two dimensions,
though, all local potentials with finite Dirichlet norm are allowed.