1977•Acta Physica SinicaOpen access

PHYSICAL METHOD OF GROUP REPRESENTATION THEORY (Ⅱ)——THE QUASI-STANDARD BASES OF PERMUTATION GROUP AND THE GELFAND BASES OF UNITARY GROUP

CHEN JIN-CHUAN, Fan Wang, Mei-Juan Gao, 南京大学物理系

Abstract

This paper analyses the contradictions which would appear when one applies the traditional theory of group repesentation to gf-the permutation group on state indicies. It is pointed out that when repeated state indicies occur, the permutation operator of gf will become undefined. According to [1], we generalise naturally the concepts of the irreducible bases for such case and give a unambiguous definition of the so called quasi-standard bases of group gf. Futhermore we have proved that the quasi-standard bases of group gf are just the Gelfand bases of group SUn. Hence the eigenfunction methodcan also be used to calculate the Gelfand bases of group SUn.

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Key concepts: Group (periodic table), Unitary group, Permutation group, Permutation (music), Mathematics, Symmetric group, Unitary state, Base (topology)