Wigner\u2019s infinite spin representations and inert matter

Bert Schroer

doi:10.1140/epjc/s10052-017-4903-9

Abstract

Positive energy ray representations of the Poincaré group are naturally subdivided into three classes according to their mass and spin content: m > 0, m=0 finite helicity and m=0 infinite spin. For a long time the localization properties of the massless infinite spin class remained unknown, until it became clear that such matter does not permit compact spacetime localization and its generating covariant fields are localized on semi-infinite space-like strings. Using a new perturbation theory for higher spin fields we present arguments which support the idea that infinite spin matter cannot interact with normal matter and we formulate conditions under which this also could happen for finite spin s>1 fields. This raises the question of a possible connection between inert matter and dark matter.

Highlights

It is not necessary that these free fields permit a characterization as Euler–Lagrange fields; the attempt to describe higher spin fields in this way and pass to quantum fields by canonical quantization or use other ways to Dedicated to the memory of Robert Schrader
Using a new perturbation theory for higher spin fields we present arguments which support the idea that infinite spin matter cannot interact with normal matter and we formulate conditions under which this could happen for finite spin s > 1 fields
Quantum gauge theory keeps some formal relation with classical gauge theory; but whereas in the classical case gauge symmetry is a bona fide local1 symmetry which is in agreement with the conceptual structure of classical field theory, the clash with the pivotal positivity

Summary

Wigner’s infinite spin representation and string-localization

Wigner’s famous 1939 theory of unitary representations of the Poincaré group P was the first systematic and successful attempt to classify relativistic particles according to the intrinsic principles of relativistic quantum theory [1]. Even more startling is the “fattening formula” which expresses the two-point function of the massive Proca potential with its 2s + 1 degrees of freedom in terms of that of the massless helicity |h| = s sl potential (or even its massless field strengths of tensor degree 2s) This flexibility between inequivalent positive energy Wigner representations is not directly visible in Wigner’s group theoretic formalism it rather requires the description of its intrinsic modular localization [9] in the form of sl fields. The physical reason why these fields are excluded from appearing in interaction densities is that there are good reasons to believe that higher order perturbation theory lead to a complete delocalization; this issue will be explained

The problem of maintaining higher order sl localization

H φ2 H

Concluding remarks