Matchete`
Matchete`
DefineCompositeCG
DefineCompositeCG[symb, {cg1, cg2, …}, {indices1, indices2, …}]
defines a new CG from the contraction (Einstein summation) of previously initialized CGs.
Details and Options
- Repeated indices describe determine how the contraction is done (as per Einstein sumation). Open indices determine the indices of the new CG (in order).
- Each set of index labels indicesn belong to the corresponding CG symbol cgn.
- The following options can be given:
-
ReplaceCGs True determines if ReplaceCGs can replace the CG with its composite constituents.
Examples
open allclose allBasic Examples (1)
Introducing a global SU(2) group automatically initializes both fundamental and adjoint representations and generator and Levi-Civita CGs:
This lets us define a new CG defined as the contraction 
of an generator of the fundamental representation with Levi-Civita tensor:
This new CG t2ε can then be used as any other CG:
The new CG is automatically decomposed with ReplaceCGs
Options (1)
ReplaceCGs (1)
The option ReplaceCGs False can be given to prevent the CG symbol defined with DefineCompostieCG from being automatically replaced with ReplaceCGs:
Tech Notes
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