Wigner Particle Theory and Local Quantum Physics

TL;DR

This paper introduces modular methods to construct local operator algebras for all positive energy Wigner representations, including exceptional cases like anyons and spin towers, bypassing traditional Lagrangian quantization.

Contribution

It develops a modular framework for directly constructing local algebras from Wigner representations, extending applicability to cases previously inaccessible to Lagrangian methods.

Findings

Constructed local operator algebras without field coordinatizations.

Extended modular methods to anyons and Wigner spin towers.

Discussed potential noncommutative spacetime formulations.

Abstract

Wigner's irreducible positive energy representations of the Poincare group are often used to give additional justifications for the Lagrangian quantization formalism of standard QFT. Here we study another more recent aspect. We explain in this paper modular concepts by which we are able to construct the local operator algebras for all standard positive energy representations directly i.e. without going through field coordinatizations. In this way the artificial emphasis on Lagrangian field coordinates is avoided from the very beginning. These new concepts allow to treat also those cases of ``exceptional'' Wigner representations associated with anyons and the famous Wigner ``spin tower''which have remained inaccessible to Lagrangian quantization. Together with the d=1+1 factorizing models (whose modular construction has been studied previously), they form an interesting family of theories with a rich vacuum-polarization structure (but no on shell real particle creation) to which the modular methods can be applied for their explicit construction. We explain and illustrate the algebraic strategy of this construction. We also comment on possibilities of formulating the Wigner theory in a setting of a noncommutative spacetime substrate. This is potentially interesting in connection with recent unitarity- and Lorentz invariance- preserving results of the special nonlocality caused by this kind of noncommutativity.