scholarly journals PARABOSE-PARAFERMI SUPERSYMMETRY

1996 ◽  
Vol 11 (16) ◽  
pp. 2957-2975 ◽  
Author(s):  
ALI MOSTAFAZADEH
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Algebraic Structure ◽  
Central Charge ◽  
Supersymmetric Quantum Mechanics ◽  
Eigenvalues And Eigenvectors ◽  
Energy Eigenvalues ◽  
General Terms ◽  
Symmetry Transformations ◽  
Definition Of

The (p=2) parabose–parafermi supersymmetry is studied in general terms. It is shown that the algebraic structure of the (p=2) parastatistical dynamical variables allows for (symmetry) transformations which mix the parabose and parafermi coordinate variables. The example of a simple parabose-parafermi oscillator is discussed and its symmetries investigated. It turns out that this oscillator possesses two parabose-parafermi supersymmetries. The combined set of generators of the symmetries forms the algebra of supersymmetric quantum mechanics supplemented with an additional central charge. In this sense there is no relation between the parabose–parafermi supersymmetry and the parasupersymmetric quantum mechanics. A precise definition of a quantum system involving this type of parabose-parafermi supersymmetry is offered, thus introducing (p=2) supersymmetric paraquantum mechanics. The spectrum degeneracy structure of general (p=2) supersymmetric paraquantum mechanics is analyzed in detail. The energy eigenvalues and eigenvectors for the parabose–parafermi oscillator are then obtained explicitly. The latter confirms the validity of the results obtained for general supersymmetric paraquantum mechanics.

Calculation of energy eigenvalues via supersymmetric quantum mechanics

1989 ◽  
Vol 67 (10) ◽  
pp. 931-934 ◽  
Author(s):  
Francisco M. Fernández ◽  
Q. Ma ◽  
D. J. DeSmet ◽  
R. H. Tipping
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Potential Energy Function ◽  
Supersymmetric Quantum Mechanics ◽  
Energy Eigenvalues ◽  
Arbitrary Power ◽  
Rational Function Approximation ◽  
Ricatti Equation ◽  
Original Potential ◽  
Ground State Energies

A systematic procedure using supersymmetric quantum mechanics is presented for calculating the energy eigenvalues of the Schrödinger equation. Starting from the Hamiltonian for a given potential-energy function, a sequence of supersymmetric partners is derived such that the ground-state energy of the kth one corresponds to the kth eigen energy of the original potential. Various theoretical procedures for obtaining ground-state energies, including a method involving a rational-function approximation for the solution of the Ricatti equation that is outlined in the present paper, can then be applied. Illustrative numerical results for two one-dimensional parity-invariant model potentials are given, and the results of the present procedure are compared with those obtainable via other methods. Generalizations of the method for arbitrary power-law potentials and for radial problems are discussed briefly.

SUPERFIELDS AND CANONICAL METHODS IN SUPERSPACE

1986 ◽  
Vol 01 (04) ◽  
pp. 293-302 ◽  
Author(s):  
J.A. DE AZCÁRRAGA ◽  
J. LUKIERSKI ◽  
P. VINDEL
Keyword(s):  
Quantum Mechanics ◽  
Evolution Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Noether’S Theorem ◽  
Equal Time ◽  
Heisenberg Picture ◽  
Noether's Theorem ◽  
Time Limits ◽  
Definition Of

We consider the “supersymmetric roots” of the Heisenberg evolution equation as describing the dynamics of superfields in superspace. We investigate the superfield commutators and their equal time limits and exhibit their noncanonical character even for free superfields. For simplicity, we concentrate on the D=1 case, i.e., the superfield formulation of supersymmetric quantum mechanics in the Heisenberg picture and, as a soluble example, the supersymmetric oscillator. Finally, we express Noether’s theorem in superspace and give the definition of the global conserved supercharges.

CONFINED LENNARD–JONES POTENTIAL: A VARIATIONAL TREATMENT

2010 ◽  
Vol 25 (08) ◽  
pp. 641-648 ◽  
Author(s):  
F. R. SILVA ◽  
E. DRIGO FILHO
Keyword(s):  
Quantum Mechanics ◽  
Variational Method ◽  
Energy Levels ◽  
Numerical Results ◽  
Supersymmetric Quantum Mechanics ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Energy Eigenvalues ◽  
Lennard Jones ◽  
Variational Treatment

In this work, the energy eigenvalues for the confined Lennard–Jones potential are calculated through the Variational Method allied to the Supersymmetric Quantum Mechanics. Numerical results are obtained for different energy levels, parameters of the potential and values of confinement radius. In the limit, where this radius assumes great values, the results for the non-confined case are recovered.

scholarly journals INDUCED VARIATIONAL METHOD FROM SUPERSYMMETRIC QUANTUM MECHANICS AND THE SCREENED COULOMB POTENTIAL

2000 ◽  
Vol 15 (19) ◽  
pp. 1253-1259 ◽  
Author(s):  
ELSO DRIGO FILHO ◽  
REGINA MARIA RICOTTA
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Variational Method ◽  
Coulomb Potential ◽  
Trial Wave Function ◽  
Supersymmetric Quantum Mechanics ◽  
Exact Results ◽  
Energy Eigenvalues ◽  
Screened Coulomb Potential

The formalism of supersymmetric quantum mechanics supplies a trial wave function to be used in the variational method. The screened Coulomb potential is analyzed within this approach. Numerical and exact results for energy eigenvalues are compared.

Dualism QM and GR

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Noncommutative Geometry ◽  
Quantum Tunneling ◽  
Closed Surface ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Surface Integral ◽  
Definition Of

Quantum tunneling of noncommutative geometry gives the definition of time in the form of holography, that is, in the form of a closed surface integral. Ultimately, the holography of time shows the dualism between quantum mechanics and the general theory of relativity.

scholarly journals Gauged double field theory as an L∞ algebra

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Eric Lescano ◽  
Martín Mayo
Keyword(s):  
Field Theory ◽  
Algebraic Structure ◽  
Classical Field ◽  
Field Theories ◽  
Lie Derivative ◽  
Linear Perturbation ◽  
Double Field Theory ◽  
Generalized Frame ◽  
Symmetry Transformations ◽  
Classical Field Theories

Abstract L∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze the algebraic structure of Gauged Double Field Theory in the generalized flux formalism. The symmetry transformations consist of a generalized deformed Lie derivative and double Lorentz transformations. We obtain all the non-trivial products in a closed form considering a generalized Kerr-Schild ansatz for the generalized frame and we include a linear perturbation for the generalized dilaton. The off-shell structure can be cast in an L3 algebra and when one considers dynamics the former is exactly promoted to an L4 algebra. The present computations show the fully algebraic structure of the fundamental charged heterotic string and the $$ {L}_3^{\mathrm{gauge}} $$ L 3 gauge structure of (Bosonic) Enhanced Double Field Theory.

scholarly journals AdS2 × S2 × CY2 solutions in Type IIB with 8 supersymmetries

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yolanda Lozano ◽  
Carlos Nunez ◽  
Anayeli Ramirez
Keyword(s):  
Quantum Mechanics ◽  
Riemann Surface ◽  
Central Charge ◽  
Global Solutions ◽  
Infinite Family ◽  
Dimensional System ◽  
One Dimensional

Abstract We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

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 Defining and Characterising Clusters in Palaeolithic Sites: a Review of Methods and Constraints

2021 ◽  
Author(s):  
Laura Sánchez-Romero ◽  
Alfonso Benito-Calvo ◽  
Joseba Rios-Garaizar
Keyword(s):  
Distribution Patterns ◽  
Horizontal Distribution ◽  
Spatial Studies ◽  
Innovative Methods ◽  
General Terms ◽  
Fabric Analysis ◽  
Gis Tools ◽  
Definition Of ◽  
Intentional Activities ◽  
Statistical Criteria

AbstractSpatial analysis studies in Palaeolithic archaeology arise as indispensable research tools for understanding archaeopalaeontological sites. In general terms, spatial studies have been specialised in the description of the distribution of materials and in the definition of accumulation areas, with the aim of distinguishing intentional activities or studying postdepositional processes. In recent decades, the development of GIS tools has enabled huge strides forward in the field of spatial archaeology research, such as spatial inferential statistics. These tools are particularly useful in the identification and location of clustering from statistical criteria, facilitating the subsequent analysis of accumulations through other archaeological, taphonomic and spatial techniques, such as fabric analysis or directional distribution. The cluster analysis, and its contextualisation considering all the archaeological and stratigraphical variables, allows the inference of some of the processes and factors that could have taken part in the accumulation of materials, as well as assessing how this affected the composition and preservation of the archaeological assemblage. The present article reviews the more traditional and innovative methods for studying horizontal distribution patterns and the objective definition of clusters, highlighting the parameters, uses and limitations of these techniques. We present an application of these methods to different Palaeolithic sites, going through different scenarios, such as location (open-air vs. cave), context, scale (large vs. small area), excavation methodology and spatial record methods.

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