scholarly journals A Specific N=2 Supersymmetric Quantum Mechanical Model: Supervariable Approach

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Aradhya Shukla
Keyword(s):  
Mechanical Model ◽  
Hodge Theory ◽  
Quantum Mechanical ◽  
Geometrical Meaning ◽  
Quantum Mechanical Model ◽  
Symmetry Transformations

By exploiting the supersymmetric invariant restrictions on the chiral and antichiral supervariables, we derive the off-shell nilpotent symmetry transformations for a specific (0 + 1)-dimensional N=2 supersymmetric quantum mechanical model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables (θ,θ¯)). We also provide the geometrical meaning to the symmetry transformations. Finally, we show that this specific N=2 SUSY quantum mechanical model is a model for Hodge theory.

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

2016 ◽  
Vol 31 (19) ◽  
pp. 1650113 ◽  
Author(s):  
S. Krishna ◽  
D. Shukla ◽  
R. P. Malik
Keyword(s):  
Differential Geometry ◽  
Mechanical Model ◽  
Magnetic Monopole ◽  
Discrete Symmetry ◽  
Quantum Mechanical ◽  
Geometrical Meaning ◽  
Quantum Mechanical Model ◽  
De Rham ◽  
Symmetry Transformations ◽  
Continuous Symmetries

In this paper, we demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting [Formula: see text] 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 [Formula: see text] 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 [Formula: see text]-dimensional supermanifold on which our [Formula: see text] 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 [Formula: see text] supercharges, and (ii) the SUSY invariance of the Lagrangian of our [Formula: see text] SUSY theory.

scholarly journals Nilpotent charges of a toy model of Hodge theory and an 𝒩 = 2 SUSY quantum mechanical model: (Anti-)chiral supervariable approach

2019 ◽  
Vol 34 (30) ◽  
pp. 1950183
Author(s):  
T. Bhanja ◽  
N. Srinivas ◽  
R. P. Malik
Keyword(s):  
General Formula ◽  
Mechanical Model ◽  
Free Particle ◽  
Brst Symmetry ◽  
Hodge Theory ◽  
Quantum Mechanical ◽  
Rigid Rotor ◽  
Quantum Mechanical Model ◽  
Evolution Parameter ◽  
Symmetry Transformations

We derive the nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations for the system of a toy model of Hodge theory (i.e. a rigid rotor) by exploiting the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti-)chiral supervariables that are defined on the appropriately chosen [Formula: see text]-dimensional super-submanifolds of the general [Formula: see text]-dimensional supermanifold on which our system of a one [Formula: see text]-dimensional (1D) toy model of Hodge theory is considered within the framework of the augmented version of the (anti-)chiral supervariable approach (ACSA) to Becchi–Rouet–Stora–Tyutin (BRST) formalism. The general [Formula: see text]-dimensional supermanifold is parametrized by the superspace coordinates [Formula: see text], where [Formula: see text] is the bosonic evolution parameter and [Formula: see text] are the Grassmannian variables which obey the standard fermionic relationships: [Formula: see text], [Formula: see text]. We provide the geometrical interpretations for the symmetry invariance and nilpotency property. Furthermore, in our present endeavor, we establish the property of absolute anticommutativity of the conserved fermionic charges which is a completely novel and surprising observation in our present endeavor where we have considered only the (anti-)chiral supervariables. To corroborate the novelty of the above observation, we apply this ACSA to an [Formula: see text] SUSY quantum mechanical (QM) system of a free particle and show that the [Formula: see text] SUSY conserved and nilpotent charges do not absolutely anticommute.

scholarly journals 𝒩 = 4 supersymmetric quantum mechanical model: Novel symmetries

2017 ◽  
Vol 32 (11) ◽  
pp. 1750055 ◽  
Author(s):  
S. Krishna
Keyword(s):  
Differential Geometry ◽  
Charged Particle ◽  
Mechanical Model ◽  
Magnetic Monopole ◽  
Discrete Symmetry ◽  
Quantum Mechanical ◽  
Quantum Mechanical Model ◽  
De Rham ◽  
Symmetry Transformations ◽  
Continuous Symmetries

We discuss a set of novel discrete symmetry transformations of the [Formula: see text] 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 [Formula: see text] SUSY transformations and provided the geometrical interpretation in the language of translational generators along the Grassmannian directions [Formula: see text] and [Formula: see text] onto [Formula: see text]-dimensional supermanifold.

scholarly journals Cold Electron Quantum Mechanical Model for Superconductivity

2015 ◽  
Vol 06 (09) ◽  
pp. 1298-1307
Author(s):  
Zhenhua Mei ◽  
Qingxian Yu ◽  
Shuyu Mei
Keyword(s):  
Mechanical Model ◽  
Quantum Mechanical ◽  
Cold Electron ◽  
Quantum Mechanical Model ◽  
Electron Quantum
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