Spinor representations for fields with any spin: Lorentz tensor basis for operators and covariant multipole decomposition

A bstract This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin ( j > 1 / 2) using chiral representations of the Lorentz group, i.e. the ( j , 0) and (0, j ) 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 2 j + 1 components needed to describe a spin- j particle. The central objects in the construction are the t -tensors, which are generalizations of the Pauli four-vector σ μ for higher spin. For the generalized spinors of these representations, we demonstrate how the algebra of the t -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 0 ≤ m ≤ 2 j 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 t -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.