Gauge equivalence of representations of symmetry groups in quantum mechanics

1978 ◽  
Vol 11 (8) ◽  
pp. 1557-1568 ◽  
Author(s):  
H Hoogland
Keyword(s):  
Quantum Mechanics ◽  
Symmetry Groups ◽  
Gauge Equivalence

Invariance Groups in Classical and Quantum Mechanics

1973 ◽  
Vol 28 (3-4) ◽  
pp. 538-540 ◽  
Author(s):  
D. J. Simms
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Energy Levels ◽  
Classical Mechanics ◽  
Symmetry Groups ◽  
Casimir Invariants ◽  
Classical Phase Space ◽  
Invariance Groups ◽  
Classical And Quantum Mechanics

AbstractThis is a report on some new relations and analogies between classical mechanics and quantum mechanics which arise out of the work of Kostant and Souriau. Topics treated are i) the role of symmetry groups; ii) the notion of elementary system and the role of Casimir invariants; iii) energy levels; iv) quantisation in terms of geometric data on the classical phase space. Some applications are described.

Representations of Groups as Automorphisms on Orthomodular Lattices and Posets

1971 ◽  
Vol 23 (4) ◽  
pp. 659-673 ◽  
Author(s):  
Stanley P. Gudder
Keyword(s):  
Quantum Mechanics ◽  
General Setting ◽  
Symmetry Groups ◽  
Orthomodular Lattices ◽  
Induced Representations ◽  
Complete Study ◽  
Logic Approach ◽  
Physical Symmetry ◽  
Groups Of Automorphisms ◽  
Axiomatic Quantum Mechanics

In this paper we study the problem of representing groups as groups of automorphisms on an orthomodular lattice or poset. This problem not only has intrinsic mathematical interest but, as we shall see, also has applications to other fields of mathematics and also physics. For example, in the “quantum logic” approach to an axiomatic quantum mechanics, important parts of the theory can not be developed any further until a fairly complete study of the representations of physical symmetry groups on orthomodular lattices is accomplished [1].We will consider two main topics in this paper. The first is the analogue of Schur's lemma and its corollaries in this general setting and the second is a study of induced representations and systems of imprimitivity.

Symmetry groups and geometrical phases in quantum mechanics

1996 ◽  
Vol 219 (3-4) ◽  
pp. 155-161 ◽  
Author(s):  
A. Cabo ◽  
J.L.M. Lucio
Keyword(s):  
Quantum Mechanics ◽  
Symmetry Groups

scholarly journals MULTIDIMENSIONAL EXACTLY SOLVABLE PROBLEMS IN QUANTUM MECHANICS AND PULLBACKS OF AFFINE COORDINATES ON THE GRASSMANNIAN

1992 ◽  
Vol 07 (07) ◽  
pp. 1449-1465 ◽  
Author(s):  
A. LOSEV ◽  
A. TURBINER
Keyword(s):  
Quantum Mechanics ◽  
Scalar Curvature ◽  
Homogeneous Space ◽  
Simple Form ◽  
Symmetry Groups ◽  
Natural Coordinates ◽  
Quadratic Polynomials ◽  
Hidden Symmetry ◽  
Exactly Solvable ◽  
Solvable Problems

Multidimensional exactly solvable problems related to compact hidden-symmetry groups are discussed. Natural coordinates on homogeneous space are introduced. It is shown that a potential and scalar curvature of the problem considered have quite a simple form of quadratic polynomials in these coordinates. A mysterious relation between the potential and the curvature observed for SU(2) in Refs. 2 and 3 is obtained in a simple way.

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