Hamiltonian reduction and supersymmetric mechanics with Dirac monopole

Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen

doi:10.1103/physrevd.74.065022

Cited by 17 publications

(12 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are various works related to the present paper: Even restricted to the recent ones, supersymmetric extensions of the Landau model [64,65,66,67,68,69], supersymmetric fuzzy manifolds [70,71], generalizations of the Hopf maps [72,73,74,75], supersymmetric quantum mechanics [76,77,78,79,80,81,82,83], and applications to string theory [84,85,86,87].…”

Section: Summary and Discussionmentioning

confidence: 99%

Hopf Maps, Lowest Landau Level, and Fuzzy Spheres

Hasebe¹

2010

SIGMA

View full text Add to dashboard Cite

Abstract. This paper is a review of monopoles, lowest Landau level, fuzzy spheres, and their mutual relations. The Hopf maps of division algebras provide a prototype relation between monopoles and fuzzy spheres. Generalization of complex numbers to Clifford algebra is exactly analogous to generalization of fuzzy two-spheres to higher dimensional fuzzy spheres. Higher dimensional fuzzy spheres have an interesting hierarchical structure made of "compounds" of lower dimensional spheres. We give a physical interpretation for such particular structure of fuzzy spheres by utilizing Landau models in generic even dimensions. With Grassmann algebra, we also introduce a graded version of the Hopf map, and discuss its relation to fuzzy supersphere in context of supersymmetric Landau model.

show abstract

Section: Summary and Discussionmentioning

confidence: 99%

Hopf Maps, Lowest Landau Level, and Fuzzy Spheres

Hasebe¹

2010

SIGMA

View full text Add to dashboard Cite

show abstract

“…Besides our present work on the N = 2 SUSY case of the charge-monopole system, there are many interesting works (see, e.g. [31][32][33][34][35][36][37][38][39][40]) on this particular system as well as that of the charge-dyon system (and their very beautiful and diverse super-extensions). For instance, it has been shown, in a couple of very interesting papers [31,32], that our present system exhibits a hidden conical dynamics.…”

Section: Discussionmentioning

confidence: 84%

Novel symmetries in an interacting 𝒩 = 2 supersymmetric quantum mechanical model

Krishna

Shukla

Malik

2016

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

We demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting N = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realizations of the de Rham cohomological operators of differential geometry. We derive the nilpotent N = 2 SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a (1, 2)-dimensional supermanifold on which our N = 2 SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables (obtained after the imposition of the SUSY invariant restrictions) and provide the geometrical meaning to (i) the nilpotency property of the N = 2 supercharges, and (ii) the SUSY invariance of the Lagrangian of our N = 2 SUSY theory.PACS numbers: 11.30.Pb, 03.65.-w, 02.40.-k Keywords: An interacting N = 2 SUSY quantum mechanical model; continuous and discrete symmetries; de Rham cohomological operators; Hodge duality operation; Hodge theory; supervariable approach; nilpotency property; geometrical interpretations * On a compact manifold without a boundary, there exists a set of three differential operators (d, δ, ∆) which are called as the de Rham cohomological operators of differential geometry. The (co-) exterior derivatives (δ)d are nilpotent of order two and their anticommutator defines the Laplacian operator ∆. They follow the algebra: d 2 = δ 2 = 0, ∆ = (d + δ) 2 = {d, δ}, [∆, d] = [∆, δ] = 0. The (co-)exterior derivatives are connected with each-other by the relationship: δ = ± * d * where the ( * ) stands for the Hodge duality operation on the given compact manifold. The Laplacian operator behaves like the Casimir operator (see, e.g. [6-10]) for this algebra.

show abstract

“…This procedure provides an elegant way of constructing non-trivial integrable models; for a recent review see [18]. This technique was applied to derive N = 4 supersymmetric mechanics in a monopole background in [19]. The connection with Killing vectors and tensors and their generalizations discussed here provides a geometrical configuration-space description of this reduction process.…”

Section: Summary and Discussionmentioning

confidence: 99%

Covariant Hamiltonian dynamics

Holten

2007

Phys. Rev. D

View full text Add to dashboard Cite

We discuss the covariant formulation of the dynamics of particles with abelian and non-abelian gauge charges in external fields. Using this formulation we develop an algorithm for the construction of constants of motion, which makes use of a generalization of the concept of Killing vectors and tensors in differential geometry. We apply the formalism to the motion of classical charges in abelian and non-abelian monopole fields. *

show abstract

Hamiltonian reduction and supersymmetric mechanics with Dirac monopole

Cited by 17 publications

References 56 publications

Hopf Maps, Lowest Landau Level, and Fuzzy Spheres

Hopf Maps, Lowest Landau Level, and Fuzzy Spheres

Novel symmetries in an interacting 𝒩 = 2 supersymmetric quantum mechanical model

Covariant Hamiltonian dynamics

Contact Info

Product

Resources

About