Representation theory of superconformal quantum mechanics

1988 ◽  
Vol 29 (5) ◽  
pp. 1163-1170 ◽  
Author(s):  
A. Bohm ◽  
M. Kmiecik ◽  
L. J. Boya
Keyword(s):  
Quantum Mechanics ◽  
Representation Theory

scholarly journals Dimensional Enhancement via Supersymmetry

2011 ◽  
Vol 2011 ◽  
pp. 1-45 ◽  
Author(s):  
M. G. Faux ◽  
K. M. Iga ◽  
G. D. Landweber
Keyword(s):  
Quantum Mechanics ◽  
Representation Theory ◽  
Gauge Invariance ◽  
Extra Dimensions ◽  
Field Theories ◽  
Consistency Test ◽  
One Dimensional ◽  
Supersymmetric Field Theories ◽  
Higher Dimensional ◽  
Supersymmetric Models

We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited, and utilized in this paper, which indicate which subset of one-dimensional supersymmetric models describes “shadows” of higher-dimensional models. This formalism delineates that minority of one-dimensional supersymmetric models which can “enhance” to accommodate extra dimensions. As a consistency test, we use our formalism to reproduce well-known conclusions about supersymmetric field theories using one-dimensional reasoning exclusively. And we introduce the notion of “phantoms” which usefully accommodate higher-dimensional gauge invariance in the context of shadow multiplets in supersymmetric quantum mechanics.

scholarly journals Models for Supersymmetric Quantum Mechanics

1991 ◽  
Vol 44 (4) ◽  
pp. 353
Author(s):  
M Baake ◽  
R Delbourgo ◽  
PD Jarvis
Keyword(s):  
Quantum Mechanics ◽  
Representation Theory ◽  
Lie Algebra ◽  
Complete Solution ◽  
Supersymmetric Quantum Mechanics ◽  
Dynamical Algebras ◽  
Model Hamiltonians

An algebraic view of supersymmetric quantum mechanics is taken, emphasising the couplings between bosonic and fermionic modes in the supercharges. A class of model Hamiltonians is introduced wherein the fermionic (bosonic) operators are canonical and the bosonic (fermionic) ones satisfy a Lie algebra (superalgebra) whose representation theory permits the complete solution of the model in principle. The kinematical symmetry of such models is also described. The examples of one and two bosonic models, with 5U(2) and 5U(3) dynamical algebras respectively, are analysed in detail.

scholarly journals From Gauge Anomalies to Gerbes and Gerbal Representations: Group Cocycles in Quantum Theory

10.14311/1189 ◽  
2010 ◽  
Vol 50 (3) ◽  
Author(s):  
J. Mickelsson
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Representation Theory ◽  
Group Cohomology ◽  
Quantum Field ◽  
Yang Mills ◽  
Gauge Anomalies

In this paper I shall discuss the role of group cohomology in quantum mechanics and quantum field theory. First, I recall how cocycles of degree 1 and 2 appear naturally in the context of gauge anomalies. Then we investigate how group cohomology of degree 3 comes from a prolongation problem for group extensions and we discuss its role in quantum field theory. Finally, we discuss a generalization to representation theory where a representation is replaced by a 1-cocycle or its prolongation by a circle, and point out how this type of situations come up in the quantization of Yang-Mills theory.

SPECTRAL THEORY INp-ADIC QUANTUM MECHANICS, AND REPRESENTATION THEORY

1991 ◽  
Vol 36 (2) ◽  
pp. 281-309 ◽  
Author(s):  
Vasilii S Vladimirov ◽  
I V Volovich ◽  
E I Zelenov
Keyword(s):  
Quantum Mechanics ◽  
Representation Theory ◽  
Spectral Theory

scholarly journals Erlangen Programme at Large 3.2 Ladder Operators in Hypercomplex Mechanics

10.14311/1402 ◽  
2011 ◽  
Vol 51 (4) ◽  
Author(s):  
V. V. Kisil
Keyword(s):  
Quantum Mechanics ◽  
Representation Theory ◽  
Harmonic Oscillator ◽  
Correspondence Principle ◽  
Free Particle ◽  
Hypercomplex Numbers ◽  
Ladder Operators ◽  
Elliptic Case ◽  
Hyperbolic Case ◽  
Parabolic Case

We revise the construction of creation/annihilation operators in quantum mechanics based on the representation theory of the Heisenberg and symplectic groups. Besides the standard harmonic oscillator (the elliptic case) we similarly treat the repulsive oscillator (hyperbolic case) and the free particle (the parabolic case). The respective hypercomplex numbers turn out to be handy on this occasion. This provides a further illustration to the Similarity and Correspondence Principle.

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