Continuous‐Representation Theory. IV. Structure of a Class of Function Spaces Arising from Quantum Mechanics

1964 ◽  
Vol 5 (7) ◽  
pp. 878-896 ◽  
Author(s):  
James McKenna ◽  
John R. Klauder
Keyword(s):  
Quantum Mechanics ◽  
Representation Theory ◽  
Function Spaces ◽  
Continuous Representation

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.

Continuous Representation Theory Using the Affine Group

1969 ◽  
Vol 10 (12) ◽  
pp. 2267-2275 ◽  
Author(s):  
Erik W. Aslaksen ◽  
John R. Klauder
Keyword(s):  
Representation Theory ◽  
Affine Group ◽  
Continuous Representation

scholarly journals Some Applications of the Spectral Theory for the Integral Transform Involving the Spectral Representation

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Hyun Soo Chung ◽  
Seung Jun Chang
Keyword(s):  
Quantum Mechanics ◽  
Function Space ◽  
Spectral Theory ◽  
Spectral Representation ◽  
Integral Transform ◽  
Adjoint Operator ◽  
Function Spaces

In many previous papers, an integral transformℱγ,βwas just considered as a transform on appropriate function spaces. In this paper we deal with the integral transform as an operator on a function space. We then apply various operator theories toℱγ,β. Finally we give an application for the spectral representation of a self-adjoint operator which plays a key role in quantum mechanics.

scholarly journals On an Inversion Operator for the Fourier Transformation

1960 ◽  
Vol 3 (2) ◽  
pp. 157-165 ◽  
Author(s):  
P. G. Rooney
Keyword(s):  
Representation Theory ◽  
Fourier Transformation ◽  
Function Spaces ◽  
Inversion Operator ◽  
Image Position

In an earlier paper [1] we presented a representation theory for the Fourier transformation defined by1.1for functions f in certain function spaces. This theory made use of an operator1.2where k = 1, 2,…, and it was stated without proof that this operator is an inversion operator for the Fourier transformation; that is, that under certain conditions1.3

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
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