Supervariable approach to nilpotent symmetries of a couple of N = 2 supersymmetric quantum mechanical models

Abstract

We derive the on-shell as well as off-shell nilpotent supersymmetric (SUSY) symmetry transformations for the N = 2 SUSY quantum mechanical model of a one (0+1)-dimensional (1D) free SUSY particle by exploiting the SUSY invariant restrictions (SUSYIRs) on the (anti-)chiral supervariables of the SUSY theory that is defined on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ andθ with θ 2 =θ 2 = 0, θθ +θθ = 0). Within the framework of our novel approach, we express the Lagrangian and conserved SUSY charges in terms of the (anti-)chiral supervariables to demonstrate the SUSY invariance of the Lagrangian as well as the nilpotency of the SUSY conserved charges in a simple manner. Our approach has the potential to be generalized to the description of other N = 2 SUSY quantum mechanical systems with physically interesting potential functions. To corroborate the above assertion, we apply our method to derive the N = 2 continuous and nilpotent SUSY transformations for one of the simplest interacting SUSY system of a 1D harmonic oscillator. PACS numbers: 11.30.Pb; Keywords: N = 2 SUSY quantum mechanics; N = 2 SUSY free particle and harmonic oscillator; on-shell and off-shell nilpotent symmetries; SUSY invariant restrictions; N = 2 SUSY algebra and its cohomological interpretation

Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta

“…It would be worthwhile to point out that, for this purpose, the well-known one (0 + 1)-dimensional (1D) model of SUSY harmonic oscillator has been taken into consideration. There is yet another SUSY quantum mechanical model which has been shown to be the physical example for the Hodge theory [20] where, once again, only three continuous symmetries exist. This is the simple toy model of N = 2 SUSY free particle.…”

(Anti)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory

“…In particular, we are very much eager to apply our method for the BRST description of the SUSY gauge theories which are important because of their relevance (i) in the context of search for the existence of the SUSY particles and (ii) as the field theoretic limiting cases of the (super)string theories. We have successfully applied our method to the description of N = 2 SUSY quantum mechanical models [29][30][31][32] but the challenge is to apply our method to the description of N = 2, 4, 8 SUSY gauge theories. We are currently busy with these ideas and we plan to report our progress in our future publications.…”

“…This is a novel feature in our present theoretical method (which thoroughly relies on the beauty and strength of the physically motivated symmetry considerations). Such methods have also been applied in the context of N = 2 SUSY quantum mechanical models [29][30][31][32] where the nilpotent N = 2 SUSY symmetry transformations have been derived. From now onwards, we shall be calling our present (anti)chiral superfield approach as the "augmented superfield formalism" for the sake of brevity but we shall always use the (anti)chiral superfields for our further discussions.…”

“…First and foremost, the symmetry invariant restrictions have played a decisive role in the derivation of the BRSTtype symmetries in the context of gauge theories (see, e.g., [33,34]) as well as N = 2 SUSY symmetries of the quantum mechanical models [29][30][31][32]. We have recently applied this method of derivation in the context of 4 Abelian 2-form gauge theory [33] as well as a 1 toy model of a rigid rotor [34].…”

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

“…We also provide the geometrical basis for the SUSY symmetry invariance of the Lagrangian of the N = 2 SUSY QM system. We lay emphasis on the fact that, to avoid the absolute anticommutativity property of the N = 2 SUSY transformations, we are theoretically compelled to choose the (anti-)chiral supervariables defined on the (1, 1)-dimensional super-submanifolds of the full (1, 2)-dimensional supermanifold [13]. The latter is parametrized by the superspace coordinate Z M = (t, θ ,θ ) with a pair of Grassmannian variables θ andθ and an evolution parameter t. The (anti-)BRST and N = 2 SUSY symmetry transformations are nilpotent of order two.…”