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On weak and strong conjugacy in the antisymmetry principle
Author(s) -
Palting Pancracio
Publication year - 1995
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560540105
Subject(s) - antisymmetry , conjugacy class , mathematics , topological conjugacy , pure mathematics , linear subspace , parity (physics) , simple (philosophy) , physics , quantum mechanics , philosophy , linguistics , epistemology
The concept of conjugate irreducible subspaces in the algebras of permutation groups is expressed in such a way that it emphasizes the existence of conjugate pathways along a chain of subgroups of permutations. The new expression is shown to be equivalent to parity conjugation and incorporates the notion of conjugate pathways in a natural and consistent manner. The example of the Aufbau chain of symmetric subgroups is used to show how the conjugacy of pathways may be useful in the symmetry adaptation of the spatial and spin parts of Fermion state functions. It is also employed to show that one may arrive at a quantitative statement that clearly expresses the conjugacy constraints placed upon a Fermion state function in order for it to satisfy the antisymmetry principle. A simple example of these conjugacy conditions is presented. © 1995 John Wiley & Sons, Inc.