General <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> supersymmetric quantum mechanical model: Supervariable approach to its off-shell nilpotent symmetries

Krishna, S.; Shukla, A.; Malik, R. P.

doi:10.1016/j.aop.2014.09.015

Cited by 15 publications

(52 citation statements)

References 25 publications

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“…We envisage to take up these challenges in our future investigations. Before we end this section, it is worthwhile to point out that in our earlier works (see, e.g., [27,28]), we have applied the techniques and tricks of ACSA to obtain the nilpotent symmetries of the N = 2 SUSY quantum mechanical models of interest. However, we have found that the conserved charges are not absolutely anticommuting.…”

Section: Discussionmentioning

confidence: 99%

Reparameterization Invariant Model of a Supersymmetric System: BRST and Supervariable Approaches

Tripathi

Chauhan

Rao

et al. 2021

Advances in High Energy Physics

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We carry out the Becchi-Rouet-Stora-Tyutin (BRST) quantization of the one 0 + 1 -dimensional (1D) model of a free massive spinning relativistic particle (i.e., a supersymmetric system) by exploiting its classical infinitesimal and continuous reparameterization symmetry transformations. We use the modified Bonora-Tonin (BT) supervariable approach (MBTSA) to BRST formalism to obtain the nilpotent (anti-)BRST symmetry transformations of the target space variables and the (anti-)BRST invariant Curci-Ferrari- (CF-) type restriction for the 1D model of our supersymmetric (SUSY) system. The nilpotent (anti-)BRST symmetry transformations for other variables of our model are derived by using the (anti-)chiral supervariable approach (ACSA) to BRST formalism. Within the framework of the latter, we have shown the existence of the CF-type restriction by proving the (i) symmetry invariance of the coupled Lagrangians and (ii) the absolute anticommutativity property of the conserved (anti-)BRST charges. The application of the MBTSA to a physical SUSY system (i.e., a 1D model of a massive spinning particle) is a novel result in our present endeavor. In the application of ACSA, we have considered only the (anti-)chiral super expansions of the supervariables. Hence, the observation of the absolute anticommutativity of the (anti-)BRST charges is a novel result. The CF-type restriction is universal in nature as it turns out to be the same for the SUSY and non-SUSY reparameterization (i.e., 1D diffeomorphism) invariant models of the (non-)relativistic particles.

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Section: Discussionmentioning

confidence: 99%

Reparameterization Invariant Model of a Supersymmetric System: BRST and Supervariable Approaches

Tripathi

Chauhan

Rao

et al. 2021

Advances in High Energy Physics

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“…Thus, we have shown that the perfect analogy between the de Rham cohomological operators of differential geometry and the N = 4 SUSY transformations (and their conserved Noether charges and Hamiltonian of the system) exists at the algebraic level, in our present investigation. In our present endeavor, we have applied supervariable approach (we have already applied this approach for different N = 2 SUSY QMMs in [15][16][17]23,24]) for the derivation of the SUSY transformations for the N = 4 SUSY QMM of a charged particle (i.e. an electron) moving on a sphere in the background of Dirac magnetic monoploe [26] within the framework of (anti-)chiral super-submanifolds.…”

Section: Discussionmentioning

confidence: 99%

𝒩 = 4 supersymmetric quantum mechanical model: Novel symmetries

Krishna

2017

Int. J. Mod. Phys. A

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We discuss a set of novel discrete symmetry transformations of the N = 4 supersymmetric quantum mechanical model of a charged particle moving on a sphere in the background of Dirac magnetic monopole. The usual five continuous symmetries (and their conserved Noether charges) and two discrete symmetries together provide the physical realizations of the de Rham cohomological operators of differential geometry. We have also exploited the supervariable approach to derive the nilpotent N = 4 SUSY transformations and provided the geometrical interpretation in the language of translational generators along the Grassmannian directions θ α andθ α onto (1, 4)-dimensional supermanifold.PACS numbers: 11.30.Pb, 03.65.-w, 02.40.-k Keywords: N = 4 SUSY QM algebra; continuous and discrete symmetries; de Rham cohomological operators; Hodge theory; supervariable approach; nilpotency property * On a compact manifold without a boundary, mathematically, there exits three differential operators (d, δ, ∆) which are called cohomological operators of differential geometry. These three de Rham cohomological operators obey the following algebra: d 2 = δ 2 = 0, ∆ = (d + δ) 2 = {d, δ}, [∆, d] = [∆, δ] = 0 where (δ)d are the (co-)exterior derivatives and ∆ is the Laplacian operator. The exterior and co-exterior derivatives together satisfy an interesting relationship: d = ± * δ * where * is the Hodge duality operation.

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“…In the above, one set of discrete symmetry transformations endow parity symmetry and the other does not, along with the time-reversal symmetry. Now, from the discrete symmetries listed in (7), concentrating on the all upper signatures only (i.e.…”

Section: Pos(ichep2020)664mentioning

confidence: 99%

Coupled N = 2 supersymmetric quantum systems: Symmetries and supervariable approach

Gupta¹,

Pradeep²,

Anjali³

et al. 2021

Proceedings of 40th International Conference on High Energy Physics — PoS(ICHEP2020)

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We consider specific examples of N = 2 supersymmetric quantum mechanical models and list out all the novel symmetries. In each case, we show the existence of two sets of discrete symmetries that correspond to the Hodge duality operator of differential geometry. Thus, we are able to provide a proof of the conjecture which endorses the existence of more than one discrete symmetry transformation as the analogue of Hodge duality operation. Finally, we extend our analysis to a more general case and derive on-shell nilpotent symmetries within the framework of supervariable approach.

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General N=2 supersymmetric quantum mechanical model: Supervariable approach to its off-shell nilpotent symmetries

Cited by 15 publications

References 25 publications

Reparameterization Invariant Model of a Supersymmetric System: BRST and Supervariable Approaches

Reparameterization Invariant Model of a Supersymmetric System: BRST and Supervariable Approaches

𝒩 = 4 supersymmetric quantum mechanical model: Novel symmetries

Coupled N = 2 supersymmetric quantum systems: Symmetries and supervariable approach

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