Matchete`
Matchete`

SimplifyCouplings

SimplifyCouplings[expr]

simplifies coupling expressions with multiple terms by identifying dummy index contractions between couplings.

Details and Options

  • SimplifyCouplings compares each coupling contraction to other contractions appearing in the same sum, bringing them on the same form if identical. It does not seek to provide a canonical form for the contraction.
  • SimplifyCouplings account for defined coupling symmetries.
  • SimplifyCouplings expands out products before attempting to identify contractions.
  • In simple cases RelabelIndices can be used to get internal dummy index labels to agree, collapsing multiple terms. However, RelabelIndices does not generate a canonical labeling of the dummy indices. Thus, there is no guarantee that mathematically identical coupling contractions are identified. For this reason SimplifyCouplings provide a more robust simplification method.

Examples

Basic Examples  (2)

Here a simple contraction of two up-type Yukawa matrices of the SM (initialized with LoadModel). SimplifyCouplings identifies the two terms in the sum:

SimplifyCouplings accounts for the (anti-)symmetries of couplings used in coupling contractions. Take the case where we add a two-index symmetric coupling S, which is contracted with the up-type Yukawa coupling:

The two terms are of the same form only when accounting for the symmetries of S.