Matchete`
Matchete`

ReplaceCGs

ReplaceCGs[expr]

replaces all CG symbols in the expression that have been defined as a contraction of other known CGs.

Details and Options

  • CG coefficients that are user defined through DefineCompositCG or have been automatically initialized in ContractCGs are replaced.
  • The internally contracted indices that appear in the contractions introduced by ReplaceCGs have unique labels. To obtain more sane names, the user may find it useful to apply RelabelIndices to the result.
  • The following options can be given:
  • CGsToReplace Alldetermines which of the candidate CGs that are replaced in the expression.
  • The option CGsToReplace takes a List of symbols.

Examples

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Basic Examples  (1)

We create a new composite CG as the contraction of two SU(3) structure constants:

When the resulting CG appears in an expression it can be written back in its constituent parts:

Options  (1)

CGsToReplace  (1)

We create a two composite CG as the contraction of two SU(3) structure constants and two symmetric tensors, respectively:

The option CGsToReplace is used to indicate that only the dd tensor should be replaced in the (list of) expression(s):

Tech Notes
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  • CG Coefficients