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The research aims to demonstrate the uniqueness of the spin-j singlet under diagonal 2I-invariance in bipartite systems.

August 9, 2026Open Access

Diagonal 2I-Invariance Selects the Universal Spin-j Singlet and Its Casimir Correlator

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The research aims to demonstrate the uniqueness of the spin-j singlet under diagonal 2I-invariance in bipartite systems.
Proved the uniqueness of the state given diagonal invariance on the carrier composed of spin-j representations.
Utilized Schur's lemma to analyze irreducible representations of the binary icosahedral group.
Computed the two-point correlator using explicit trace formulas.
Identified the state as the unique 2SU(2) singlet, confirmed up to phase.
Derivation of the correlator yields E(hat{a},hat{b}) = -3(j(j+1)/3)(hat{a}dothat{b}).
Demonstrated limitations of group invariance in deriving additional quantum properties.

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Conditional theorem establishes unique spin-j singlet and correlator in bipartite systems, highlighting group-invariance implications.

Jérôme Beau (2026) studied this question.

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