XCOLOR: Color factor in some ﬁeld theories
Date: 2020-10-07 18:10:00

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### 16.80 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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