Open AccessPHYSICAL METHODS OF GROUP REPRESENTATION THEORY (Ⅰ)——A NEW APPROACH TO THE THEORY OF FINITE GROUP REPRESENTATIONS
Author(s) -
Jinquan Chen,
Fan Wang,
Ming Gao
Publication year - 1977
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.26.307
Subject(s) - group (periodic table) , group representation , representation (politics) , representation theory of finite groups , algebra over a field , irreducible representation , group theory , representation theory , set (abstract data type) , representation theory of su , matrix (chemical analysis) , restricted representation , computer science , mathematics , pure mathematics , fundamental representation , physics , quantum mechanics , lie algebra , materials science , composite material , politics , political science , weight , law , programming language
This paper advocates a new approach to the theory of finite group representa-tions by applying exclusively the method of commuting operators in quantum me-chanics. The basic problems of group representation theory such as the labeling of irreducible representations, the finding of characters, irreducible bases and matrix ele-ments and the CG coefficients et al are all simplified to the solving of the eigenfunc-tions of a certain complete set of commuting operators. This method has the advan-tage of being concise in theory and easily manageable in practice.