Matchete`
Matchete`

DefineRepresentation

DefineRepresentation[repName, groupName, rep]

initializes a representation repName associated to the groupName group

Details and Options

  • DefineRepresentation does not give a return value, but modifies the internal state of Matchete, initializing a new representation associated with a group has been initialized through DefineCGGroup, DefineGaugeGroup, or DefineGlobalGroup.
  • All representations are initialized with a Kronecker delta CG for that representation, which is named del[repName].
  • All representations associated with a gauge or global group are initialized with a generator CG for that representation, which is named gen[repName].
  • Representations are labeled with a list of integers corresponding to the Dynkin coefficients of the highest weight in the representation.
  • The algebra argument must be a valid Alg[class, n] object.
  • The following options can be given:
  • IndexAlphabet Nonespecifies a canoncial printing alphabet for the representation under NiceForm.
  • The option IndexAlphabet takes a list of strings (typically characters).

Examples

open allclose all

Basic Examples  (1)

Initializing the adjoint representation adj of an SU(2) group G1:

The representation also initializes the Kronecker delta CG for the adj representation:

Options  (1)

IndexAlphabet  (1)

The formatting of the canonical index names d$$1, d$$2, … (as used for dummy indices under RelabelIndices) can be specified with the IndexAlphabet option. Here we have a fundamental representation of an SU(3) use double-struck letters:

Tech Notes
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  • CG Coefficients
    • ▪
    Group Magic