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Δ I = 1/2‐Rule and Fierz‐, SU (3)‐ and Colour SU (3)‐Crossing Eigenvectors of the Current‐Current Quark Interaction
Author(s) -
Körner J. G.
Publication year - 1975
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19750231104
Subject(s) - physics , octet , hamiltonian (control theory) , eigenvalues and eigenvectors , quark , hadron , particle physics , current (fluid) , quark model , quantum mechanics , mathematics , quarkonium , mathematical optimization , thermodynamics
In this review we study the SU (3) transformation behaviour of the hadronic current‐current quark interaction Hamiltonian for the different cases of possible quark statistics. By expanding the current‐current quark Hamiltonian along the crossing‐even and ‐odd eigenvectors of the appropiate Fierz‐, SU (3)‐ and colour SU (3)‐crossing matrices, resp., we arrive at a transparent classification of the possible forms of the current‐current quark interaction that lead to octet behaviour. In some instances, octet behaviour can be established directly for the interaction Hamiltonian, in others, simplifications occur if one makes reference to the two basic types of diagrams that occur in the evaluation of nonleptonic transitions.