Spinor Representations for Fields with any Spin: Lorentz Tensor Basis for Operators and Covariant Multipole Decomposition
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| Format: | Preprint |
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2025
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| _version_ | 1866908710087950336 |
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| author | Cosyn, Wim Vera, Frank |
| author_facet | Cosyn, Wim Vera, Frank |
| contents | 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 $σ^μ$ 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 $0\leq m \leq 2j$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_22046 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spinor Representations for Fields with any Spin: Lorentz Tensor Basis for Operators and Covariant Multipole Decomposition Cosyn, Wim Vera, Frank High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory 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 $σ^μ$ 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 $0\leq m \leq 2j$ 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. |
| title | Spinor Representations for Fields with any Spin: Lorentz Tensor Basis for Operators and Covariant Multipole Decomposition |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2503.22046 |