Z2×Z2 -graded parastatistics in multiparticle quantum Hamiltonians

  title={Z2×Z2 -graded parastatistics in multiparticle quantum Hamiltonians},
  author={Francesco Toppan},
  journal={Journal of Physics A: Mathematical and Theoretical},
  • F. Toppan
  • Published 26 August 2020
  • Physics
  • Journal of Physics A: Mathematical and Theoretical
The recent surge of interest in Z2×Z2 -graded invariant mechanics poses the challenge of understanding the physical consequences of a Z2×Z2 -graded symmetry. In this paper it is shown that non-trivial physics can be detected in the multiparticle sector of a theory, being induced by the Z2×Z2 -graded parastatistics obeyed by the particles. The toy model of the N=4 supersymmetric/ Z2×Z2 -graded oscillator is used. In this set-up the one-particle energy levels and their degenerations are the same… 

Z23-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics

  • S. DoiN. Aizawa
  • Physics, Mathematics
    Symmetry, Integrability and Geometry: Methods and Applications
  • 2021
Quantum mechanical systems whose symmetry is given by Z2-graded version of superconformal algebra are introduced. This is done by finding a realization of a Z2-graded Lie superalgebra in terms of a

Inequivalent quantizations from gradings and Z2×Z2 parabosons

  • F. Toppan
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2021
This paper introduces the parastatistics induced by Z2×Z2‐graded algebras. It accommodates four kinds of particles: ordinary bosons and three types of parabosons which mutually anticommute when

Classification of minimal Z2×Z2-graded Lie (super)algebras and some applications

This paper presents the classification, over the fields of real and complex numbers, of the minimal Z2 × Z2-graded Lie algebras and Lie superalgebras spanned by 4 generators and with no empty graded

Irreducible representations of Z 22 -graded N = 2 supersymmetry algebra and Z 22 -graded supermechanics

Irreducible representations (irreps) of Z 2 2 -graded supersymmetry algebra of N = 2 are obtained by the method of induced representation and they are used to derive Z 22 -graded supersymmetric

Irreducible representations of Z22-graded N=2 supersymmetry algebra and Z22-graded supermechanics

Irreducible representations (irreps) of [Formula: see text]-graded supersymmetry algebra of [Formula: see text] are obtained by the method of induced representation, and they are used to derive

First quantization of braided Majorana fermions

A Z 2 -graded qubit represents an even (bosonic) “vacuum state” and an odd, excited, Majorana fermion state. The multiparticle sectors of N , braided, indistinguishable Majorana fermions are

First quantization of braided Majorana fermions

Beyond the 10-fold way: 13 associative Z 2 × Z 2 -graded superdivision algebras

The “10-fold way” refers to the combined classification of the 3 associative division algebras (of real, complex and quaternionic numbers) and of the 7, Z2-graded, superdivision algebras (in a

The Z2×Z2 -graded Lie superalgebras pso(2n+1|2n) and pso(∞|∞) , and parastatistics Fock spaces

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

Beyond the $10$-fold way: $13$ associative $Z_2\times Z_2$-graded superdivision algebras

The “10-fold way” refers to the combined classification of the 3 associative division algebras (of real, complex and quaternionic numbers) and of the 7, Z2-graded, superdivision algebras (in a



${\mathbb Z}_2\times {\mathbb Z}_2$-graded mechanics: the quantization

In the previous paper arXiv:2003.06470 we introduced the notion of ${\mathbb Z}_2\times{\mathbb Z}_2$-graded classical mechanics and presented a general framework to construct, in the Lagrangian

${\mathbb{Z}}_{2}{\times}{\mathbb{Z}}_{2}$-graded supersymmetry: 2-d sigma models

We propose a natural $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded generalisation of $d=2$, $\mathcal{N}=(1,1)$ supersymmetry and construct a $\mathbb{Z}_2^2$-space realisation thereof. Due to the

$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$-graded mechanics: the classical theory

$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$-graded mechanics admits four types of particles: ordinary bosons, two classes of fermions (fermions belonging to different classes commute among each

$\mathbb{Z}_2\times \mathbb{Z}_2$-graded Lie symmetries of the Lévy-Leblond equations

The first-order differential L\'evy-Leblond equations (LLE's) are the non-relativistic analogs of the Dirac equation, being square roots of ($1+d$)-dimensional Schr\"odinger or heat equations. Just

Z2n-graded extensions of supersymmetric quantum mechanics via Clifford algebras

It is shown that the ${\cal N}=1$ supersymmetric quantum mechanics (SQM) can be extended to a $\mathbb{Z}_2^n$-graded superalgebra. This is done by presenting quantum mechanical models which realize,

Riemannian Structures on Z 2 n -Manifolds

Very loosely, $\mathbb{Z}_2^n$-manifolds are `manifolds' with $\mathbb{Z}_2^n$-graded coordinates and their sign rule is determined by the scalar product of their $\mathbb{Z}_2^n$-degrees. A little

Super-de Sitter and Alternative Super-Poincaré Symmetries

It is well-known that de Sitter Lie algebra \(\mathfrak{o}(1,4)\) contrary to anti-de Sitter one \(\mathfrak{o}(2,3)\) does not have a standard \(\mathbb{Z}_{2}\)-graded superextension. We show here

Z2*Z2-graded Lie symmetries of the Levy-Leblond equations

This paper exhaustively investigates the symmetries of the $(1+1)$-dimensional L\'evy-Leblond Equations, both in the free case and for the harmonic potential, and introduces a new feature, explaining the existence of first-order differential symmetry operators not entering the super Schr\"odinger algebra.

N-extension of double-graded supersymmetric and superconformal quantum mechanics

In the recent paper (Bruce and Duplij 2019 (arXiv:1904.06975 [math-ph])), Bruce and Duplij introduced a double-graded version of supersymmetric quantum mechanics (SQM). It is an extension of Lie

Do the Equations of Motion Determine the Quantum Mechanical Commutation Relations

The commutator of the Hamiltonian with the operator corresponding to any physical quantity gives the operator which corresponds to the time derivative of that quantity. One can ask, hence, whether