Conformal parasuperalgebras and their realizations on the line

Durand, Stéphane; Floreanini, Roberto; Mayrand, Michel; Vinet, Luc

doi:10.1016/0370-2693(89)90633-3

Cited by 23 publications

(18 citation statements)

References 2 publications

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“…It is worth adding here that historically the PSQM of order 2 was introduced rst [106] and its various consequences were discussed [238,239,240,241,242]. Initially it was felt that the generalization to order p was not possible in the sense that the PSQM of order p cannot be characterized with one universal algebraic relation [243].…”

Section: Bound States In the Continuummentioning

confidence: 99%

Supersymmetry and quantum mechanics

1995

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In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a m uch deeper understanding of why certain potentials are analytically solvable and an array o f p o w erful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all 1 have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Approximation methods are also discussed within the framework of supersymmetric quantum mechanics and in particular it is shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate in a double well potential and for improving large N expansions. We also discuss the problem of a charged Dirac particle in an external magnetic eld and other potentials in terms of supersymmetric quantum mechanics. Finally, w e discuss structures more general than supersymmetric quantum mechanics such as parasupersymmetric quantum mechanics in which there is a symmetry between a boson and a para-fermion of order p.

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Section: Bound States In the Continuummentioning

confidence: 99%

Supersymmetry and quantum mechanics

1995

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“…Ref. [13] has attempted at a more systematic consideration of the algebraic aspects of PGA based on the Green ansatz (see, e.g. [14]) and introduced, in that frame, a sort of paragrassmann generalization of the conformal algebra.…”

Section: Introductionmentioning

confidence: 99%

Paragrassmann differential calculus

Филиппов¹,

Исаев²,

Kurdikov³

1993

Theor Math Phys

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This paper significantly extends and generalizes our previous paper [1]. Here we discuss explicit general constructions for paragrassmann calculus with one and many variables. For one variable, nondegenerate differentiation algebras are identified and shown to be equivalent to the algebra of (p+1)×(p+1) complex matrices. If (p+1) is prime integer, the algebra is nondegenerate and so unique. We then give a general construction of the many-variable differentiation algebras. Some particular examples are related to the multi-parametric quantum deformations of the harmonic oscillators. * Address until Dec.22, 1992: Yukawa Inst. Theor. Phys., Kyoto Univ.,

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“…For p f even, the φ(x, y) can be written as in (17). For p f odd, the φ(x, y) is given by (21), with gcd (ψ + , ψ − ) written as (24) through the relation of (22).…”

Section: Discussionmentioning

confidence: 99%

“…Historically, the homogeneous polynomial relation between the general parasupercharge Q and Hamiltonian H was first introduced as a parasuperalgebra [17], which is given by generalizing the grassmannian variable θ in the ordinary superalgebra to the paragrassmannian such that θ p+1 = 0 (for p ∈ N). Under the maps H → ∂/∂t and Q → ∂/∂θ + θ · ∂/∂t (in the Euclidean space with t ∈ R), H and Q correspond to the superconformal generators L 1 and G 1/2 , respectively.…”

Section: Conformalitymentioning

confidence: 99%

Minimum Polynomial for Single-Mode Parabose Parasupercharge and Hamiltonian

Kuwata

2009

Int J Theor Phys

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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) satisfies the homogeneity ∀λ ∈ R, φ(λx, λ 2 y) = λ n φ(x, y), then the parafermionic order p f is restricted to either 1, 2, or 4. Under the P-PSUSY, the homogeneity of the φ(x, y) is equivalent to the parasuperconformality of Q and H . The physical meaning of the parasuperconformality is discussed, in connection with the spin of the elementary particle.

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Conformal parasuperalgebras and their realizations on the line

Cited by 23 publications

References 2 publications

Supersymmetry and quantum mechanics

Supersymmetry and quantum mechanics

Paragrassmann differential calculus

Minimum Polynomial for Single-Mode Parabose Parasupercharge and Hamiltonian

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