Mixed symmetry gauge fields in a flat background

TL;DR

The paper classifies covariant, finite-component wave equations for free relativistic particles in flat spacetime of arbitrary dimension $D$, linking them to Poincaré group representations. It presents Bargmann-Wigner's theorem using a curvature-based construction to connect harmonic multiform solutions with massless UIRs and the corresponding physical Hilbert spaces. It analyzes massive and massless cases: massive fields satisfy transversality and tracelessness to realize $O(D-1,1)$ irreps, while massless fields rely on gauge symmetry and curvature-based equations (Fronsdal/Labastida, with non-local Francia-Sagnotti reformulations) to obtain $O(D-2)$ irreps. Together these results extend Fierz-Pauli's programme to arbitrary dimensions and mixed-symmetry tensors, providing a unified framework for higher-spin gauge theories and their potential interactions.

Abstract

We present a list of all inequivalent bosonic covariant free particle wave equations in a flat spacetime of arbitrary dimension. The wave functions are assumed to have a finite number of components. We relate these wave equations to equivalent versions obtained following other approaches.