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The $Z_2 \times Z_2$-graded Lie superalgebras $pso(2n+1|2n)$ and $pso(\infty|\infty)$, and parastatistics Fock spaces
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abstract
The parastatistics Fock spaces of order $p$ corresponding to an infinite number of parafermions and parabosons with relative paraboson relations are constructed. The Fock spaces are lowest weight representations of the $Z_2 \times Z_2$-graded Lie superalgebra $pso(\infty|\infty)$, with a basis consisting of row-stable Gelfand-Zetlin patterns.
Forward citations
Cited by 3 Pith papers
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Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework
Color Heisenberg-Lie (super)algebras graded by Z3×Z3 provide a unified framework for mixed-bracket parabosons and parafermions, reproducing s=3,6 braided Majorana qubit truncations and a new two-particle density signature.
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On the detectability of paraparticles beyond bosons and fermions
The paper argues that Z2xZ2-graded paraparticles are theoretically detectable through two-particle observables, and sketches a minimal experimental protocol.
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On braid statistics versus parastatistics
A report on results that claim to refute the conventionality of parastatistics using 2-bit paraparticles, plus a review of braided Majorana qubits for topological quantum computation.
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