Showing papers on "Equivalence class published in 1976"

On local and global equivalence of wave functions

Abstract: Unitary continuous projective representations of symmetry groups operating in Hilbert spaces of one-particle wave functions are studied from the point of view of physical equivalence, which does not always agree with projective equivalence. Global and local equivalence between projective representations is defined and the local equivalence classes within a given global equivalence class are determined from group-theoretical properties, especially the exponents of the symmetry group. Examples are given of cosmological symmetry groups describing one-dimensional models of universes, where a free particle respectively a particle in a uniform external field are described by projectively equivalent representations of the symmetry group, which are globally but not locally equivalent.

Quotients of Group Algebrae in the Calculation of Intermediate Ligand Field Matrix Elements

Abstract: The structure of the classes of symmetry elements excluded during the subduction of the representations of SU(2) onto the finite group 0* is shown to quantitatively define the relationship of the coupling algebrae of these two groups. This relationship is formalized as a quotient algebra. This quotient algebra is realized as 3Γ-like symbols which exist whether or not the quotient can be defined as a group. These symbols distribute the value of a reduced matrix element of SU(2) onto the subduced reduced matrix elements of O* and are termed Partition Coefficients. Since the structure of the excluded symmetry classes is independent of the quantization of O*, these Partition Coefficients can be used to define the values of the matrix elements of O* without reference to the form of its basis set. Thus, the choice of physical interpretation of the ligand field is unimportant. The strong field, weak field, Russell-Saunders and j-j coupling models are all unified in terms of the Partition Coefficients and the 3Γ symbols which are appropriate to the quantization.

Classes of points of cubic hypersurfaces defined over finite fields

Abstract: The points of a cubic hypersurface are divided into equivalence classes of Ya. I. Manin [1]. It is established that the quasigroup of these equivalence classes over a finite field is isomorphic to either 1 or Z2 or Z3 under some weak conditions.

Spaces defined by sequences

Abstract: The biquotient, countably biquotient, hereditarily quotient, and quotient images of ^-spaces are classified. Also, the quotient images of paracompact M-spaces, and the quotient images of A/-spaces are classified without any separation axioms. New definitions are given for certain familiar classes of spaces to give the definitions more uniformity.