Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

TURKISH JOURNAL OF PHYSICS

Quantization of Paraclassical Systems and Parabose- Parafermi Supersymmetry

Ali MOSTAFAZADEH

Published Jan 1, 1997• 0 citations
Publisher

Abstract

A convenient formalism is developed to treat classical dynamical systems involving (p = 2) parafermionic and parabosonic dynamical variables. This is achieved via the introduction of a parabracket which summarizes the para-commutation relations of the corrosponding Green components in a unified manner. The formalism is used to investigate the supersymmetries of a system consisting of a (p= 2) parabose and a (p=2) parafermi oscillator. This suggests a definition for supersymmetric paraquantum mechanics of order p=2. For such systems the degeneracy strucure of the spectrum is also analyzed.

DOI
10.55730/1300-0101.2382

Related papers

PARABOSE-PARAFERMI SUPERSYMMETRY

ALI MOSTAFAZADEH

The (p=2) parabose–parafermi supersymmetry is studied in general terms. It is shown that the algebraic structure of the (p=2) parastatistical dynamical variables allows for (symmetry) transformations which mix the parabose and parafermi coordinate variables. The example of a simple parabose-parafermi oscillator is discussed and its symmetries investigated. It turns out that this oscillator possesses two parabose-parafermi supersymmetries. The combined set of generators of the symmetries forms the algebra of supersymmetric quantum mechanics supplemented with an additional central charge. In this sense there is no relation between the parabose–parafermi supersymmetry and the parasupersymmetric quantum mechanics. A precise definition of a quantum system involving this type of parabose-parafermi supersymmetry is offered, thus introducing (p=2) supersymmetric paraquantum mechanics. The spectrum degeneracy structure of general (p=2) supersymmetric paraquantum mechanics is analyzed in detail. The energy eigenvalues and eigenvectors for the parabose–parafermi oscillator are then obtained explicitly. The latter confirms the validity of the results obtained for general supersymmetric paraquantum mechanics.

arXiv:hep-th/9508106•International Journal of Modern Physics A•Jun 30, 1996•9 citations

Algebraic structure of parabose Fock space. I. The Green’s ansatz revisited

Alan Macfarlane

A description of the Fock space of a parabose oscillator of order p based on commutation relations bilinear in creation and annihilation operators rather than trilinear ones is developed. A new statement of the well-known Green’s ansatz is introduced to help understand the significance of the bilinear commutation relations. It is also applied to show how all parabose oscillators of even order (respectively, odd order) can be obtained as irreducible constituents of the Fock space associated with a Green’s ansatz of two (three) terms. Analogs of the form in which the parabose Green’s ansatz is presented are provided for one parafermi oscillator and for systems of many parabose and parafermi oscillators of the same order. Methods used in the paper allow various new results for q-deformed parabose oscillators to be derived.

Journal of Mathematical Physics•Mar 1, 1994•59 citations

Path integrals for parastatistics

Oscar Wallace Greenberg, A. K. Mishra

We demonstrate that parastatistics can be quantized using path integrals by calculating the generating functionals for time-ordered products of both free and interacting parabose and parafermi fields in terms of path integrals. We also give a convenient form of the commutation relations for the Green components of the parabose and parafermi operators in both the canonical and path integral formalisms.

arXiv:math-ph/0406011•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Dec 21, 2004•11 citations

Bosonized supersymmetric quantum mechanics and supersymmetry of parabosons (parafermions)

Mikhail S. Plyushchay

We review the construction of minimally bosonized supersymmetric quantum mechanics and its relation to hidden supersymmetries in pure parabosonic (parafermionic) systems.

•Jan 16, 2000•0 citations

Bosonized supersymmetric quantum mechanics and supersymmetry of parabosons (parafermions)

Mikhail S. Plyushchay

We review the construction of minimally bosonized supersymmetric quantum mechanics and its relation to hidden supersymmetries in pure parabosonic (parafermionic) systems.

arXiv:hep-th/0001094•Jan 16, 2000•0 citations

SUPERSYMMETRIC PARA BOSON-FERMION OSCILLATOR SYSTEMS AND THEIR SPECTRA

Mitsuru Hama, ARATA KOIKE, MAKOTO SAWAMURA +1 more

Para boson-fermion supersymmetry is exemplified in simple oscillator systems. The parasupercharge satisfies the ordinary supersymmetry algebra. The parabosonic and parafermionic oscillators do not commute and the energy spectra are non-trivial for even the one level system. We calculate the partition functions and compare with those for the non-supersymmetric systems.

Modern Physics Letters A•Jul 20, 1991•3 citations
A convenient formalism is developed to treat classical dynamical systems involving (p = 2) parafermionic and parabosonic dynamical variables. This is achieved via the introduction of a parabracket which summarizes the para-commutation relations of the corrosponding Green components in a unified manner. The formalism is used to investigate the supersymmetries of a system consisting of a (p= 2) parabose and a (p=2) parafermi oscillator. This suggests a definition for supersymmetric paraquantum mechanics of order p=2. For such systems the degeneracy strucure of the spectrum is also analyzed.
The (p=2) parabose–parafermi supersymmetry is studied in general terms. It is shown that the algebraic structure of the (p=2) parastatistical dynamical variables allows for (symmetry) transformations which mix the parabose and parafermi coordinate variables. The example of a simple parabose-parafermi oscillator is discussed and its symmetries investigated. It turns out that this oscillator possesses two parabose-parafermi supersymmetries. The combined set of generators of the symmetries forms the algebra of supersymmetric quantum mechanics supplemented with an additional central charge. In this sense there is no relation between the parabose–parafermi supersymmetry and the parasupersymmetric quantum mechanics. A precise definition of a quantum system involving this type of parabose-parafermi supersymmetry is offered, thus introducing (p=2) supersymmetric paraquantum mechanics. The spectrum degeneracy structure of general (p=2) supersymmetric paraquantum mechanics is analyzed in detail. The energy eigenvalues and eigenvectors for the parabose–parafermi oscillator are then obtained explicitly. The latter confirms the validity of the results obtained for general supersymmetric paraquantum mechanics.
A description of the Fock space of a parabose oscillator of order p based on commutation relations bilinear in creation and annihilation operators rather than trilinear ones is developed. A new statement of the well-known Green’s ansatz is introduced to help understand the significance of the bilinear commutation relations. It is also applied to show how all parabose oscillators of even order (respectively, odd order) can be obtained as irreducible constituents of the Fock space associated with a Green’s ansatz of two (three) terms. Analogs of the form in which the parabose Green’s ansatz is presented are provided for one parafermi oscillator and for systems of many parabose and parafermi oscillators of the same order. Methods used in the paper allow various new results for q-deformed parabose oscillators to be derived.