Transmuted spectrum-generating algebras and detectable parastatistics of the Superconformal Quantum Mechanics

Abstract

In a recent paper (Balbino-de Freitas-Rana-FT, arXiv:2309.00965) we proved that the supercharges of the supersymmetric quantum mechanics can be statistically transmuted and accommodated into a $Z_2^n$-graded parastatistics. In this talk I derive the $6=1+2+3$ transmuted spectrum-generating algebras (whose respective $Z_2^n$ gradings are $n=0,1,2$) of the $\mathcal{N}=2$ Superconformal Quantum Mechanics. These spectrum-generating algebras allow to compute, in the corresponding multiparticle sectors of the de Alfaro-Fubini-Furlan deformed oscillator, the degeneracies of each energy level. The levels induced by the $Z_2\times Z_2$-graded paraparticles cannot be reproduced by the ordinary bosons/fermions statistics. This implies the theoretical detectability of the $Z_2\times Z_2$-graded parastatistics.

7 pages; in the proceedings of XII International Symposium on Quantum Theory and Symmetries - QTS12, Prague, July 2023

References in corpus (10)

• Once more on parastatistics
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded parastatistics in multiparticle quantum Hamiltonians
• Quantum simulation of driven para-Bose oscillators
• Inequivalent quantizations from gradings and ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ parabosons
• Classification of minimal ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded Lie (super)algebras and some applications
• Minimal bosonization of double-graded supersymmetric quantum mechanics
• Paraboson quotients. A braided look at Green ansatz and a generalization
• New aspects of the Z${}_{\text{2}}$ $\times$ Z${}_{\text{2}}$-graded 1D superspace: induced strings and 2D relativistic models
• Experimental realization of para-particle oscillators
• The $Z_2\times Z_2$-graded Lie superalgebras $pso(2n+1|2n)$ and $pso(\infty |\infty )$, and parastatistics Fock spaces

Cited by in corpus (3)

• Integrable ${\mathbb{Z}}_2^2$-graded Extensions of the Liouville and Sinh-Gordon Theories
• On the detectability of paraparticles beyond bosons and fermions
• On braid statistics versus parastatistics