scholarly journals Higher-Dimensional SUSY Quantum Mechanics

1997 ◽  
Vol 12 (08) ◽  
pp. 581-588 ◽  
Author(s):  
A. Das ◽  
S. Okubo ◽  
S. A. Pernice
Keyword(s):  
Quantum Mechanics ◽  
Spin Structure ◽  
Supersymmetric Quantum Mechanics ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Supersymmetry Algebra ◽  
General Properties ◽  
Higher Dimensional ◽  
Spatial Dimensions

Higher-dimensional supersymmetric quantum mechanics is studied. General properties of the two-dimensional case are presented. For three spatial dimensions or higher, a spin structure is shown to arise naturally from the nonrelativistic supersymmetry algebra.

A Graphical Exposition of the Ising Problem

1971 ◽  
Vol 12 (3) ◽  
pp. 365-377 ◽  
Author(s):  
Frank Harary
Keyword(s):  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Higher Dimensional ◽  
The One

Ising [1] proposed the problem which now bears his name and solved it for the one-dimensional case only, leaving the higher dimensional cases as unsolved problems. The first solution to the two dimensional Ising problem was obtained by Onsager [6]. Onsager's method was subsequently explained more clearly by Kaufman [3]. More recently, Kac and Ward [2] discovered a simpler procedure involving determinants which is not logically complete.

scholarly journals Integrable and Superintegrable Systems with Higher Order Integrals of Motion: Master Function Formalism

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Z. Alizadeh ◽  
H. Panahi
Keyword(s):  
Quantum Mechanics ◽  
Higher Order ◽  
Supersymmetric Quantum Mechanics ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Function Formalism ◽  
Superintegrable Systems ◽  
Master Function

We construct two-dimensional integrable and superintegrable systems in terms of the master function formalism and relate them to Mielnik’s and Marquette’s construction in supersymmetric quantum mechanics. For two different cases of the master functions, we obtain two different two-dimensional superintegrable systems with higher order integrals of motion.

scholarly journals AN ALTERNATIVE DIMENSIONAL REDUCTION PRESCRIPTION

1996 ◽  
Vol 11 (13) ◽  
pp. 1037-1045 ◽  
Author(s):  
J.D. EDELSTEIN ◽  
C. NÚÑEZ ◽  
F.A. SCHAPOSNIK ◽  
J.J. GIAMBIAGI
Keyword(s):  
Dimensional Reduction ◽  
Dimensional Space ◽  
Dimensional Case ◽  
Green Functions ◽  
Two Dimensional ◽  
Spatial Coordinate ◽  
Higher Dimensional

We propose an alternative dimensional reduction prescription which in respect with Green functions corresponds to dropping the extra spatial coordinate. From this, we construct the dimensionally reduced Lagrangians both for scalars and fermions, discussing bosonization and supersymmetry in the particular two-dimensional case. We argue that our proposal is in some situations more physical in the sense that it maintains the form of the interactions between particles thus preserving the dynamics corresponding to the higher-dimensional space.

Supersymmetric quantum mechanics for two-dimensional disk

Pramana ◽  
2005 ◽  
Vol 65 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Akira Suzuki ◽  
Ranabir Dutt ◽  
Rajat K. Bhaduri
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
Two Dimensional

Shadowing property of geodesics in Hedlund's metric

1997 ◽  
Vol 17 (1) ◽  
pp. 187-203 ◽  
Author(s):  
MARK LEVI
Keyword(s):  
Geodesic Flow ◽  
Rotation Vector ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Shadowing Property ◽  
Mather Theory ◽  
Higher Dimensional

In this paper we show that the geodesic flow in a Hedlund-type metric on the 3-torus possesses the shadowing property. This implies, in particular, that any rotation vector is represented by a geodesic, a fact that in the two-dimensional case is given by the Aubry–Mather theory, while in the higher-dimensional case is still unknown.

scholarly journals On two-dimensional superpotentials: from classical Hamilton–Jacobi theory to 2D supersymmetric quantum mechanics

2004 ◽  
Vol 37 (43) ◽  
pp. 10323-10338 ◽  
Author(s):  
A Alonso Izquierdo ◽  
M A Gonzalez Leon ◽  
M de la Torre Mayado ◽  
J Mateos Guilarte
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
Two Dimensional

scholarly journals The Velocity Tensor and the Momentum Tensor

10.14311/1356 ◽  
2011 ◽  
Vol 51 (2) ◽  
Author(s):  
T. Lanczewski
Keyword(s):  
Momentum Tensor ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Higher Dimensional ◽  
Velocity Tensor

This paper introduces a new object called the momentum tensor. Together with the velocity tensorit forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are derived as well as its relation with the velocity tensor. For the sake of clarity only two-dimensional case is investigated. However, general conclusions are also valid for higher dimensional spacetimes.

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