1211.2831 (Peter Morgan)

Nonlinear Wightman fields    [PDF]

Peter Morgan

There have been many attempts in the literature to modify the Wightman or Haag-Kastler axioms to be closer to the empirically successful Lagrangian and related approaches to quantum field theory. Insofar as one fundamental difficulty of both Wightman and Lagrangian QFT is the postulate that the quantum field is an operator-valued distribution ---a linear map from a linear space of test functions to a linear space of Hilbert space operators--- together with the introduction of products of the quantum field, we are motivated to consider taking a quantum field to be a nonlinear map from a linear space of test functions to a linear space of operators, an approach not previously proposed. Constructively, two nonlinear possibilities for the scalar field case are introduced and discussed, the first of which offers a fresh perspective on renormalization while the second widens the range of well-defined theories enough that they may provide worthwhile effective field models.

View original: http://arxiv.org/abs/1211.2831