Matchete`
Matchete`

CG

CG[cgName, {indexLabel1, indexLabel2, …}]

is a user short-hand for inputting a Clebsch-Gordan coefficient.

CG[cgName, {Index[label1, rep1], …}]

is the internal representation of a Clebsch-Gordan coefficient.

cgName[indexLabel1, indexLabel2, …]

is an ergonomic user short-hand to input CGs.

Details and Options

  • A user input of a CG coefficient only needs to specify the name of the coefficient and a list of labels for the indices. This is automatically converted to the full internal representation.
  • The internal representation of a CG coefficient consists of the name of the coefficient and a list of indices in full Index form.
  • CG is conveniently formatted under NiceForm without all the detailed information of the internal representation.

Examples

Basic Examples  (1)

Initializing a global SU(3) group G automatically initializes the associated structure constants fStruct[G]:

The structure constant CG with its three indices can be input as

Observe how the CG is immediately turned into the full internal representation upon input. The NiceForm display format is more suitable for human sight.

The most ergonomic way for the user to input a CG is to refer directly to its name:

Tech Notes
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  • CG Coefficients