Nonlinear Wightman fields

TL;DR

This paper introduces nonlinear Wightman fields as maps from test functions to operators, exploring two approaches that offer new perspectives on renormalization and a broad class of nonlinear quantum theories.

Contribution

It develops two frameworks for nonlinear quantum fields, one based on Lagrangian QFT and the other on linear Wightman fields, expanding the theoretical landscape.

Findings

Two approaches to nonlinear quantum fields are constructed.

The Lagrangian approach offers a new perspective on renormalization.

The second approach provides a wide range of well-defined nonlinear theories.

Abstract

A nonlinear Wightman field is taken to be a nonlinear map from a linear space of test functions to a linear space of Hilbert space operators, with inessential modifications to other axioms only to the extent dictated by the introduction of nonlinearity. Two approaches to nonlinear quantum fields are constructed and discussed, the first of which, starting from Lagrangian QFT, offers a fresh perspective on renormalization, while the second, starting from linear Wightman fields, provides an extensive range of well-defined nonlinear theories.