paper

Spinor Representations for Fields with any Spin: Lorentz Tensor Basis for Operators and Covariant Multipole Decomposition

arXiv:2503.22046 · doi:10.1007/JHEP12(2025)068

Abstract

This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin using chiral representations of the Lorentz group, i.e. the and representations and their parity-invariant direct sum. Unlike traditional approaches that require imposing constraints to eliminate spurious degrees of freedom, these chiral representations contain exactly the components needed to describe a spin- particle. The central objects in the construction are the -tensors, which are generalizations of the Pauli four-vector for higher spin. For the generalized spinors of these representations, we demonstrate how the algebra of the -tensors allows to formulate a generalization of the Dirac matrix basis for any spin. For on-shell bilinears, we show that a set consisting exclusively of covariant multipoles of order forms a complete basis. We provide explicit expressions for all bilinears of the generalized Dirac matrix basis, which are valid for any spin value. As a byproduct of our derivations we present an efficient algorithm to compute the -tensor matrix elements. The formalism presented here paves the way to use a more unified approach to analyze the non-perturbative QCD structure of hadrons and nuclei across different spin values, with clear physical interpretation of the resulting distributions as covariant multipoles.

v2: 54 pages, 3 figures; matches published version; added correspondence with massive helicity spinors, improved notation, clarified discussion

References in corpus (13)