scholarly journals MINIMAL BOSONIZATION OF SUPERSYMMETRY

1996 ◽  
Vol 11 (05) ◽  
pp. 397-408 ◽  
Author(s):  
MIKHAIL S. PLYUSHCHAY
Keyword(s):  
Quantum Mechanics ◽  
Symmetry Algebra ◽  
Dynamical Symmetry ◽  
Degree Of Freedom ◽  
Supersymmetric Quantum Mechanics ◽  
Supersymmetric Extension ◽  
Calogero Model ◽  
Parity Operator ◽  
Relationship Of ◽  
Bosonic Oscillator

The minimal bosonization of supersymmetry in terms of one bosonic degree of freedom is considered. A nontrivial relationship of the construction to the Witten supersymmetric quantum mechanics is illustrated with the help of the simplest N=2 SUSY system realized on the basis of the ordinary (undeformed) bosonic oscillator. It is shown that the generalization of such a construction to the case of Vasiliev deformed bosonic oscillator gives a supersymmetric extension of the two-body Calogero model in the phase of exact or spontaneously broken N=2 SUSY. The construction admits an extension to the case of the OSp(2|2) supersymmetry, and, as a consequence, osp(2|2) superalgebra is revealed as a dynamical symmetry algebra for the bosonized supersymmetric Calogero model. Realizing the Klein operator as a parity operator, we construct the bosonized Witten supersymmetric quantum mechanics. Here the general case of the corresponding bosonized N=2 SUSY is given by an odd function being a superpotential.

Generalized Electromagnetic Fields Associated with the Hydrogen-Like Atom Problem

2018 ◽  
Vol 74 (1) ◽  
pp. 43-50 ◽  
Author(s):  
S.A. Bruce ◽  
J.F. Diaz-Valdes
Keyword(s):  
Quantum Mechanics ◽  
Electromagnetic Coupling ◽  
Relativistic Quantum ◽  
Scalar Potential ◽  
Symmetry Algebra ◽  
Dynamical Symmetry ◽  
Canonical Commutation Relation ◽  
Quantum Systems ◽  
Minimal Coupling ◽  
Exactly Solvable

AbstractIt is known that the principle of minimal coupling in quantum mechanics determines a unique interaction form for a charged particle. By properly redefining the canonical commutation relation between (canonical) conjugate components of position and momentum of the particle, e.g. an electron, we restate the Dirac equation for the hydrogen-like atom problem incorporating a generalized minimal electromagnetic coupling. The corresponding interaction keeps the $1/\left|\mathbf{q}\right|$ dependence in both the scalar potential $V\left({\left|\mathbf{q}\right|}\right)$ and the vector potential $\mathbf{A}\left(\mathbf{q}\right)$ ($\left|{\mathbf{A}\left(\mathbf{q}\right)}\right|\sim 1/\left|\mathbf{q}\right|$). This problem turns out to be exactly solvable; moreover, the eigenstates and eigenvalues can be obtained in an elementary fashion. Some feasible models within this approach are discussed. Then we make a few remarks about the breaking of supersymmetry. Finally, we briefly comment on the possible Lie algebra (dynamical symmetry algebra) of these relativistic quantum systems.

scholarly journals Dynamical symmetry algebra of the Calogero model

2001 ◽  
Vol 511 (2-4) ◽  
pp. 276-284 ◽  
Author(s):  
L. Jonke ◽  
S. Meljanac
Keyword(s):  
Symmetry Algebra ◽  
Dynamical Symmetry ◽  
Calogero Model

scholarly journals Minimal bosonization of double-graded quantum mechanics

2021 ◽  
Vol 36 (33) ◽  
Author(s):  
C. Quesne
Keyword(s):  
Quantum Mechanics ◽  
Central Element ◽  
Degree Of Freedom ◽  
Supersymmetric Quantum Mechanics ◽  
Oscillator Algebra ◽  
Deformed Oscillator ◽  
Deformed Oscillator Algebra

The superalgebra of [Formula: see text]-graded supersymmetric quantum mechanics is shown to be realizable in terms of a single bosonic degree of freedom. Such an approach is directly inspired by a description of the corresponding [Formula: see text]-graded superalgebra in the framework of a Calogero–Vasiliev algebra or, more generally, of a generalized deformed oscillator algebra. In the case of the [Formula: see text]-graded superalgebra, the central element [Formula: see text] has the property of distinguishing between degenerate eigenstates of the Hamiltonian.

scholarly journals ABCD of ’t Hooft operators

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Takuya Okuda ◽  
Yutaka Yoshida
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Type Ii ◽  
Expectation Values ◽  
String Theories

Abstract We compute by supersymmetric localization the expectation values of half-BPS ’t Hooft line operators in $$ \mathcal{N} $$ N = 2 U(N ), SO(N ) and USp(N ) gauge theories on S1 × ℝ3 with an Ω-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the ’t Hooft operators using branes and orientifolds in type II string theories.

scholarly journals Local G2-manifolds, Higgs bundles and a colored quantum mechanics

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Max Hübner
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Higgs Bundle ◽  
Higgs Bundles ◽  
View Point ◽  
Yang Mills ◽  
G2 Manifolds ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

scholarly journals Wronskian differential formula for confluent supersymmetric quantum mechanics

2012 ◽  
Vol 376 (5) ◽  
pp. 692-696 ◽  
Author(s):  
David Bermudez ◽  
David J. Fernández C. ◽  
Nicolás Fernández-García
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics

A Golden-Thompson inequality in supersymmetric quantum mechanics

1991 ◽  
Vol 21 (3) ◽  
pp. 237-244 ◽  
Author(s):  
Slawomir Klimek ◽  
Andrzej Lesniewski
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics
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