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

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2]
  1. Florida International Univ. (FIU), Miami, FL (United States)
  2. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Florida International Univ. (FIU), Miami, FL (United States)
+ Show Author Affiliations
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 2j + 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 σμ 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 ≤ 2j 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.
Research Organization:
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE Office of Science (SC), Nuclear Physics (NP)
Grant/Contract Number:
AC05-06OR23177
OSTI ID:
3011639
Report Number(s):
DOE/OR/23177--7820; JLAB-THY--25-4259; arXiv:2503.22046
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2025; ISSN 1029-8479
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English

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