20.63 XCOLOR: Color Factor in some Field Theories

This package calculates the color factor in non-abelian gauge field theories using an algorithm due to Cvitanovich.

Documentation for this package is in plain text.

Author: A. Kryukov.

Program "xCOLOR" is intended for calculation the colour factor in non-abelian gauge field theories. It is realized Cvitanovich algorithm [Cvi76]. In comparison to the program "COLOR" [KR88] many improvements were made. The package was written in symbolic mode. This version is more than \(10\) times faster than the one in [KR88].

After load the program by the following command load xcolor;
user can be able to use the next additional commands and operators.

Command SUdim.

Format: SUdim <any expression>;
Set the order of SU group.
The default value is 3, i.e. SU(3).

Command SpTT.

Format: SpTT <any expression>;
Set the normalization coefficient A: Sp(TiTj) = A*Delta(i,j). Default value is 1/2.

Operator QG.

Format: QG(inQuark,outQuark,Gluon)
Describe the quark-gluon vertex. Parameters may be any identifiers. First and second of then must be in- and out- quarks correspondently. Third one is a gluon.

Operator G3.

Format: G3(Gluon1,Gluon2,Gluon3)
Describe the three-gluon vertex. Parameters may be any identifiers. The order of gluons must be clock.
In terms of QG and G3 operators you input diagram in "color" space as a product of these operators. For example.

 Diagram:                       REDUCE expression:

            e1

         ---->---
        /        \
       |    e2    |
     v1*..........*v2  <===>  QG(e3,e1,e2)*QG(e1,e3,e2)
       |          |
        \   e3   /
         ----<---


Here: --->--- quark

      ....... gluon

For more detail see [KR88].

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