INDUCED REPRESENTATIONS OF GROUPS AND QUANTUM MECHANICS

1970 ◽  
Vol 2 (2) ◽  
pp. 246-247
Author(s):  
R. F. Streater
Keyword(s):  
Quantum Mechanics ◽  
Induced Representations ◽  
Representations Of Groups

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.

Restriction of irreducible representations of groups to a subgroup

1971 ◽  
Vol 322 (1549) ◽  
pp. 181-189 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Irreducible Representation ◽  
Symmetry Breaking ◽  
Irreducible Representations ◽  
Representations Of Groups ◽  
Group Play ◽  
Special Case

The number and character of the irreducible representations of a subgroup, contained in an irreducible representation of the whole group (if this representation is restricted to the sub­ group) play an important role in quantum mechanics. They give the number and type of the states, generated by a symmetry breaking perturbation, from a state which has the symmetry of the whole group. Three equations are derived here for the number and character of the representations of the subgroup, resulting from the restriction of the irreducible represen­tations of the whole group. These equations contain an earlier rule as a special case.

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