JOURNAL OF MATHEMATICAL PHYSICS, ISSN 0022-2488, 10/2018, Volume 59, Issue 10

In this paper, we consider the mth order Cauchy-Euler's differential equation involving a para-Grassmann variable of order p. In the Grassmann case (i.e., p =...

PARA-FERMI SYSTEMS | ALGEBRAS | PARASUPERSYMMETRIC QUANTUM-MECHANICS | FRACTIONAL SUPERSYMMETRY | EXTENSION | PHYSICS, MATHEMATICAL

PARA-FERMI SYSTEMS | ALGEBRAS | PARASUPERSYMMETRIC QUANTUM-MECHANICS | FRACTIONAL SUPERSYMMETRY | EXTENSION | PHYSICS, MATHEMATICAL

Journal Article

Physics Letters A, ISSN 0375-9601, 06/2019, Volume 383, Issue 17, pp. 1989 - 1996

In this paper, we consider the particle obeying the Wigner algebra which we call a Wignon. First, we study the single mode Wignon algebra and its...

The Wigner algebra | The supersymmetric quantum mechanics | The Hamiltonian of wignon | FOCK SPACE | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | PARASUPERSYMMETRIC QUANTUM-MECHANICS | EQUATIONS | SYSTEMS | DEFORMED HEISENBERG ALGEBRA

The Wigner algebra | The supersymmetric quantum mechanics | The Hamiltonian of wignon | FOCK SPACE | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | PARASUPERSYMMETRIC QUANTUM-MECHANICS | EQUATIONS | SYSTEMS | DEFORMED HEISENBERG ALGEBRA

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 5/2017, Volume 2017, Issue 5, pp. 1 - 40

Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to...

Discrete Symmetries | Random Systems | Lattice Integrable Models | Extended Supersymmetry | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | MODELS | THERMALIZATION | PARASUPERSYMMETRIC QUANTUM-MECHANICS | INDEX | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Supersymmetry | Chains | Correlators | Entangled states | Nuclear and particle physics. Atomic energy. Radioactivity | Condensed Matter - Statistical Mechanics | High Energy Physics - Theory | Condensed Matter - Disordered Systems and Neural Networks

Discrete Symmetries | Random Systems | Lattice Integrable Models | Extended Supersymmetry | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | MODELS | THERMALIZATION | PARASUPERSYMMETRIC QUANTUM-MECHANICS | INDEX | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Supersymmetry | Chains | Correlators | Entangled states | Nuclear and particle physics. Atomic energy. Radioactivity | Condensed Matter - Statistical Mechanics | High Energy Physics - Theory | Condensed Matter - Disordered Systems and Neural Networks

Journal Article

Annals of Physics, ISSN 0003-4916, 08/2010, Volume 325, Issue 8, pp. 1679 - 1707

We continue the previous study on the existence of different intermediate Hamiltonians in type A N-fold supersymmetric systems and carry out an exhaustive...

Parasupersymmetry | Generalized superalgebra | Intertwining operators | Shape invariance | N-fold supersymmetry | Quasi-solvability | 2ND-ORDER | PHYSICS, MULTIDISCIPLINARY | PARASUPERSYMMETRIC QUANTUM-MECHANICS | MANY-BODY SYSTEMS

Parasupersymmetry | Generalized superalgebra | Intertwining operators | Shape invariance | N-fold supersymmetry | Quasi-solvability | 2ND-ORDER | PHYSICS, MULTIDISCIPLINARY | PARASUPERSYMMETRIC QUANTUM-MECHANICS | MANY-BODY SYSTEMS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 04/2010, Volume 51, Issue 4, pp. 043512 - 043512-21

Linear differential equations with constant coefficients involving a para-Grassmann variable have been considered recently in the work of Mansour and Schork...

D=2(1/3,1/3) SUPERSYMMETRIC THEORIES | DEFORMED HEISENBERG-ALGEBRA | 2-POINT FUNCTIONS | PARA-FERMI SYSTEMS | STATES | FRACTIONAL SUPERSPACE FORMULATION | PARASUPERSYMMETRIC QUANTUM-MECHANICS | CONFORMAL FIELD-THEORIES | FOUNDATIONS | PHYSICS, MATHEMATICAL | ALTERNATIVE STATISTICS

D=2(1/3,1/3) SUPERSYMMETRIC THEORIES | DEFORMED HEISENBERG-ALGEBRA | 2-POINT FUNCTIONS | PARA-FERMI SYSTEMS | STATES | FRACTIONAL SUPERSPACE FORMULATION | PARASUPERSYMMETRIC QUANTUM-MECHANICS | CONFORMAL FIELD-THEORIES | FOUNDATIONS | PHYSICS, MATHEMATICAL | ALTERNATIVE STATISTICS

Journal Article

Annals of Physics, ISSN 0003-4916, 2009, Volume 324, Issue 11, pp. 2438 - 2451

Type A -fold supercharge admits a one-parameter family of factorizations into product of first-order linear differential operators due to an underlying...

Parasupersymmetry | [formula omitted]-fold supersymmetry | Pöschl–Teller potentials | Intertwining operators | Factorization method | Pöschl-Teller potentials | N-fold supersymmetry | DERIVATIVE SUPERSYMMETRY | REAL SPECTRUM | 2ND-ORDER | PHYSICS, MULTIDISCIPLINARY | POTENTIALS | OSCILLATOR | SYMMETRY | PARASUPERSYMMETRIC QUANTUM-MECHANICS | GENERAL FORMALISM | MANY-BODY SYSTEMS | Poschl-Teller potentials | Geometry | Mathematics | Algebra | Particle physics | FACTORIZATION | HAMILTONIANS | SUPERSYMMETRY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Parasupersymmetry | [formula omitted]-fold supersymmetry | Pöschl–Teller potentials | Intertwining operators | Factorization method | Pöschl-Teller potentials | N-fold supersymmetry | DERIVATIVE SUPERSYMMETRY | REAL SPECTRUM | 2ND-ORDER | PHYSICS, MULTIDISCIPLINARY | POTENTIALS | OSCILLATOR | SYMMETRY | PARASUPERSYMMETRIC QUANTUM-MECHANICS | GENERAL FORMALISM | MANY-BODY SYSTEMS | Poschl-Teller potentials | Geometry | Mathematics | Algebra | Particle physics | FACTORIZATION | HAMILTONIANS | SUPERSYMMETRY | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Journal Article

International Journal of Theoretical Physics, ISSN 0020-7748, 6/2009, Volume 48, Issue 6, pp. 1813 - 1832

We calculate the minimum polynomial φ(x,y) of parasupercharge Q and Hamiltonian H for single-mode parabose parasupersymmetry (P-PSUSY). Suppose that φ(x,y)...

Parasuperconformality | Gröbner basis | Mathematical and Computational Physics | Parasupersymmetry | Quantum Physics | Physics, general | Neveu-Schwarz | Physics | Elementary Particles, Quantum Field Theory | Grobner basis | PARASTATISTICS | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | PARASUPERSYMMETRIC QUANTUM-MECHANICS | REALIZATIONS

Parasuperconformality | Gröbner basis | Mathematical and Computational Physics | Parasupersymmetry | Quantum Physics | Physics, general | Neveu-Schwarz | Physics | Elementary Particles, Quantum Field Theory | Grobner basis | PARASTATISTICS | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | PARASUPERSYMMETRIC QUANTUM-MECHANICS | REALIZATIONS

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2009, Volume 5, p. 073

As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and...

Para-grassmann variables | Linear differential equations | DEFORMED HEISENBERG-ALGEBRA | STATES | FRACTIONAL SUPERSPACE FORMULATION | EXTENSION | PHYSICS, MATHEMATICAL | D=2(1/3,1/3) SUPERSYMMETRIC THEORIES | 2-POINT FUNCTIONS | PARA-FERMI SYSTEMS | PARASUPERSYMMETRIC QUANTUM-MECHANICS | para-Grassmann variables | CONFORMAL FIELD-THEORIES | linear differential equations | ALTERNATIVE STATISTICS

Para-grassmann variables | Linear differential equations | DEFORMED HEISENBERG-ALGEBRA | STATES | FRACTIONAL SUPERSPACE FORMULATION | EXTENSION | PHYSICS, MATHEMATICAL | D=2(1/3,1/3) SUPERSYMMETRIC THEORIES | 2-POINT FUNCTIONS | PARA-FERMI SYSTEMS | PARASUPERSYMMETRIC QUANTUM-MECHANICS | para-Grassmann variables | CONFORMAL FIELD-THEORIES | linear differential equations | ALTERNATIVE STATISTICS

Journal Article

Physics Letters A, ISSN 0375-9601, 2000, Volume 265, Issue 1, pp. 20 - 27

It is shown that shape invariance on the main quantum number n introduces a bunch of superpotentials, and, consequently, derives some quantum solvable systems...

Para-supersymmetry | Superpotential | Shape invariance | para-supersymmetry | MATHEMATICAL PHYSICS | ORDER | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | SOLVABLE POTENTIALS | PARASUPERSYMMETRIC QUANTUM-MECHANICS | DIFFERENTIAL-EQUATIONS | shape invariance | superpotential

Para-supersymmetry | Superpotential | Shape invariance | para-supersymmetry | MATHEMATICAL PHYSICS | ORDER | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | SOLVABLE POTENTIALS | PARASUPERSYMMETRIC QUANTUM-MECHANICS | DIFFERENTIAL-EQUATIONS | shape invariance | superpotential

Journal Article

Modern Physics Letters A, ISSN 0217-7323, 01/2002, Volume 17, Issue 3, pp. 131 - 140

We investigate a quantum system possessing a parasupersymmetry of order 2, an orthosupersymmetry of order p, a fractional supersymmetry of order p+1, and...

Parasupersymmetry | Supersymmetry | Orthofermions | Fractional supersymmetry | supersymmetry | ORDER | fractional supersymmetry | PARASUPERSYMMETRIC QUANTUM-MECHANICS | orthofermions | PHYSICS, NUCLEAR | parasupersymmetry | FOUNDATIONS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Parasupersymmetry | Supersymmetry | Orthofermions | Fractional supersymmetry | supersymmetry | ORDER | fractional supersymmetry | PARASUPERSYMMETRIC QUANTUM-MECHANICS | orthofermions | PHYSICS, NUCLEAR | parasupersymmetry | FOUNDATIONS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Journal Article

Modern Physics Letters A, ISSN 0217-7323, 01/2000, Volume 15, Issue 3, pp. 175 - 184

We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying...

SUPERSYMMETRY | SINGER INDEX THEOREM | PARASUPERSYMMETRIC QUANTUM-MECHANICS | PHYSICS, NUCLEAR | PHYSICS, MATHEMATICAL | DEFORMATION | MORSE-THEORY | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

SUPERSYMMETRY | SINGER INDEX THEOREM | PARASUPERSYMMETRIC QUANTUM-MECHANICS | PHYSICS, NUCLEAR | PHYSICS, MATHEMATICAL | DEFORMATION | MORSE-THEORY | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory

Journal Article

Physics Letters A, ISSN 0375-9601, 1997, Volume 232, Issue 6, pp. 399 - 408

In the paper we give a consecutive description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey...

PHYSICS, MULTIDISCIPLINARY | PARASUPERSYMMETRIC QUANTUM-MECHANICS

PHYSICS, MULTIDISCIPLINARY | PARASUPERSYMMETRIC QUANTUM-MECHANICS

Journal Article

Journal of Physics A: Mathematical and General, ISSN 0305-4470, 10/2004, Volume 37, Issue 43, pp. 10193 - 10207

We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce...

PT-SYMMETRY | TOPOLOGICAL INVARIANTS | WITTEN INDEX | REAL SPECTRUM | PHYSICS, MULTIDISCIPLINARY | SUSY ALGEBRA | PARASUPERSYMMETRIC QUANTUM-MECHANICS | SINGER INDEX THEOREM | FRACTIONAL SUPERSYMMETRY | HAMILTONIANS | PHYSICS, MATHEMATICAL | CPT-INVARIANCE

PT-SYMMETRY | TOPOLOGICAL INVARIANTS | WITTEN INDEX | REAL SPECTRUM | PHYSICS, MULTIDISCIPLINARY | SUSY ALGEBRA | PARASUPERSYMMETRIC QUANTUM-MECHANICS | SINGER INDEX THEOREM | FRACTIONAL SUPERSYMMETRY | HAMILTONIANS | PHYSICS, MATHEMATICAL | CPT-INVARIANCE

Journal Article

Journal of Physics A: Mathematical and General, ISSN 0305-4470, 12/2000, Volume 33, Issue 47, pp. 8525 - 8547

We describe irreducible representations of the extended Poincare parasuperalgebra (PPSA) which includes an arbitrary number N of parasupercharges, n (n less...

SUPERSYMMETRY | PARTICLE | PARASUPERSYMMETRIC QUANTUM-MECHANICS | MODEL | RULES | PHYSICS, MATHEMATICAL | IRREDUCIBLE REPRESENTATIONS

SUPERSYMMETRY | PARTICLE | PARASUPERSYMMETRIC QUANTUM-MECHANICS | MODEL | RULES | PHYSICS, MATHEMATICAL | IRREDUCIBLE REPRESENTATIONS

Journal Article

Journal of Physics A: Mathematical and General, ISSN 0305-4470, 07/1999, Volume 32, Issue 27, pp. 5141 - 5155

We classify and explicitly construct all the irreducible hermitian representations of the extended Poincare parasuperalgebra. These representations which...

PARASTATISTICS | BREAKING | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | PARASUPERSYMMETRIC QUANTUM-MECHANICS

PARASTATISTICS | BREAKING | SUPERSYMMETRY | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | PARASUPERSYMMETRIC QUANTUM-MECHANICS

Journal Article

Journal of Physics A: Mathematical and General, ISSN 0305-4470, 01/2000, Volume 33, Issue 2, pp. 293 - 305

Equations of shape invariance have been derived on the homogeneous SL(2, c)/GL(1, c), by means of which the Dirac equation is solved for a charged spin-1/2...

ORDER | SUPERSYMMETRY | PHYSICS, MATHEMATICAL | SOLVABLE POTENTIALS | SHAPE INVARIANCE | PARASUPERSYMMETRIC QUANTUM-MECHANICS

ORDER | SUPERSYMMETRY | PHYSICS, MATHEMATICAL | SOLVABLE POTENTIALS | SHAPE INVARIANCE | PARASUPERSYMMETRIC QUANTUM-MECHANICS

Journal Article

Journal of Physics A: Mathematical and General, ISSN 0305-4470, 03/1995, Volume 28, Issue 6, pp. 1655 - 1668

We explicitly describe all the irreducible unitary representations of the Poincare parasuperalgebra, i.e. the parasupersymmetric extension of the Lie algebra...

BREAKING | SUPERSYMMETRIZATION PROCEDURE | PHYSICS, MATHEMATICAL | PARASUPERSYMMETRIC QUANTUM-MECHANICS | LIE STRUCTURES

BREAKING | SUPERSYMMETRIZATION PROCEDURE | PHYSICS, MATHEMATICAL | PARASUPERSYMMETRIC QUANTUM-MECHANICS | LIE STRUCTURES

Journal Article

2003, INSTITUTE OF PHYSICS CONFERENCE SERIES, Volume 173, 4

We review various generalizations of supersymmetry and discuss their relationship. In particular, we show how supersymmetry, parasupersymmetry, fractional...

FORMS | SYMMETRIES | PHYSICS, MULTIDISCIPLINARY | STATISTICS | INVARIANTS | PARASUPERSYMMETRIC QUANTUM-MECHANICS | SINGER INDEX THEOREM | FRACTIONAL SUPERSYMMETRY | FOUNDATIONS

FORMS | SYMMETRIES | PHYSICS, MULTIDISCIPLINARY | STATISTICS | INVARIANTS | PARASUPERSYMMETRIC QUANTUM-MECHANICS | SINGER INDEX THEOREM | FRACTIONAL SUPERSYMMETRY | FOUNDATIONS

Book Chapter

Physical Review D - Particles, Fields, Gravitation and Cosmology, ISSN 1550-7998, 11/2015, Volume 92, Issue 10

Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a more consistent approach to the derivation of the third order wave equation obtained earlier...

PARA-FERMI SYSTEMS | SUPERSYMMETRY | PARA-GRASSMANN ALGEBRAS | QUANTUM GROUPS | ASTRONOMY & ASTROPHYSICS | PARASUPERSYMMETRIC SPINNING PARTICLE | TOPOLOGICAL GAUGE-FIELDS | COMMUTATION RELATIONS | PATH-INTEGRAL REPRESENTATION | DEFORMED HEISENBERG ALGEBRA | CUBIC ROOT | PHYSICS, PARTICLES & FIELDS | Construction | Algebra | Roots | Wave equations | Differential equations | Wave functions | Gages | Gauges | Physics - High Energy Physics - Theory

PARA-FERMI SYSTEMS | SUPERSYMMETRY | PARA-GRASSMANN ALGEBRAS | QUANTUM GROUPS | ASTRONOMY & ASTROPHYSICS | PARASUPERSYMMETRIC SPINNING PARTICLE | TOPOLOGICAL GAUGE-FIELDS | COMMUTATION RELATIONS | PATH-INTEGRAL REPRESENTATION | DEFORMED HEISENBERG ALGEBRA | CUBIC ROOT | PHYSICS, PARTICLES & FIELDS | Construction | Algebra | Roots | Wave equations | Differential equations | Wave functions | Gages | Gauges | Physics - High Energy Physics - Theory

Journal Article

20.
Para-超對稱量子力學

本篇論文主要在討論如何建構出等價的 Parasupersymmetric Quantum Mechanics (PSQM) 的公式以及探討其所代表的物理意義。首先, 略為回顧 Supersymmetric Quantum Mechanics (SQM), 以為討論 PSQM 的準備。 接下來的章節, 我們將熟悉的...

超對稱量子力學 | Para-超對稱量子力學 | Supersymmetric Quantum Mechanics | Parasupersymmetric Quantum Mechanics

超對稱量子力學 | Para-超對稱量子力學 | Supersymmetric Quantum Mechanics | Parasupersymmetric Quantum Mechanics

Dissertation

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