Elsevier Science Home
Computer Physics Communications Program Library
Full text online from Science Direct
Programs in Physics & Physical Chemistry
CPC Home

[Licence| Download | New Version Template] acvy_v1_0.gz(56 Kbytes)
Manuscript Title: Pascal program for generating tables of SU(3) Clebsch-Gordan coefficients.
Authors: T.A. Kaeding
Program title: SU3Clebsch
Catalogue identifier: ACVY_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 85(1995)82
Programming language: Pascal.
Computer: VAX workstation 4090.
Operating system: VMS v. T6.1.
RAM: 4000K words
Word size: 32
Keywords: General purpose, Elementary particle physics, Algebras, QCD, SU(3), Clebsch-Gordan coefficients.
Classification: 4.2, 11.5.

Nature of problem:
Calculations in models based on the group SU(3) often require Clebsch- Gordan coefficients in the product of group representations. Previously compiled tables [1] contained only representations having integral hypercharge values. They are therefore useful for calculations involving mesons and hadrons, but are inadequate for calculations that involve arbitrary numbers of quarks.

Solution method:
The program generates representations of SU(3) whose states are represented by vectors. The dimension of such a vector is the number of SU(3) tensor indicies used to describe the representation. The vectors in the product of two representations are formed by taking outer products. The set of such vectors in decomposed into the irreducible representations of the Clebsch-Gordan series. The Clebsch-Gordan coefficients are then found as inner products between the initial set of vectors and the states in this decomposition.

Restrictions:
The program is written to handle representations that have at most nine SU(3) indicies. For most physical calculations this should suffice.

Unusual features:
The program does not compile a general table of coefficients. However, the calculation of many tables of coefficients has been written into the program. If the user needs any other tables, he is encouraged to follow the examples in the code in order to write other routines.

Running time:
Running time depends on which table is compiled. Times quoted are for the VAX 4090. For 3bar times 3, the CPU time is 4.3 sec. For 10bar times 8, the CPU time is 52 min 26 sec.

References:
[1] P. McNamee and F. Chilton, Rev. Mod. Phys. 36(1964)1005.