Matchete`
Matchete`

ContractCGs

ContractCGs[expr]

evaluates all contractions of CGs occurring in the expression.

Details and Options

  • ContractCGs will expand the expression before doing contractions in each term separately.
  • ContractCGs finds each disjoint contraction of CGs in a terms, replaces the CGs with the numerical tensors and performs a tensor contraction to evaluate the Einstein summation of the indices. The resulting tensor is (attempted) projected onto a basis of previously defined CGs. If this is not possible (i.e. if the previously defined CGs do not form a basis), a new CG is initialized instead. Please refer to CG Coefficients for examples.

Examples

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Basic Examples  (2)

Two generators of the fundamental representation of SU(3) contracts to form a Kronecker delta:

Full contractions of CGs evaluates to numbers:

Scope  (4)

ContractCGs expands the expression it is applied to and applies to each term separately:

It will correctly identify situations where the result is a tensor product of CGs, such as for the ordinary Fierz identities:

When the resulting CG is not in the basis of defined CGs, a new CG is initialized:

More details of what to do in such situations is found in CG Coefficients.

ContractCGs threads over List, treating each entry as an individual expression:

Tech Notes
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  • CG Coefficients