Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
LieART`
DecomposeIrrep |
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Examples
(3)
Basic Examples
(2)
Decompose the of SU(5) to SU(3)⊗SU(2)⊗U(1):
10
In[1]:=
DecomposeIrrep[Irrep[SU5][Bar[10]],ProductAlgebra[SU3,SU2,U1]]
Out[1]=
(1,1)(6)+(3,1)(-4)+(,2)(1)
3
In[2]:=
DecomposeIrrep[{Irrep[SU5][10],Irrep[SU5][Bar[5]]},ProductAlgebra[SU3,SU2,U1]]
Out[2]=
{(,1)(4)+(3,2)(-1)+(1,1)(-6),(,1)(-2)+(1,2)(3)}
3
3
Decompose the SU(3) irrep 3 of (24,3)(-3) of SU(5)⊗SU(3)⊗U(1) to SU(2)⊗U'(1), i.e. SU(5)⊗SU(3)⊗U(1)SU(5)⊗SU(2)⊗U'(1)⊗U(1):
In[1]:=
DecomposeIrrep[ProductIrrep[Irrep[SU5][24],Irrep[SU3][3],Irrep[U1][-3]],ProductAlgebra[SU2,U1],2]
Out[1]=
(24,1)(-2)(-3)+(24,2)(1)(-3)
The same decomposition as above displayed as branching rule:
In[2]:=
Rule[#,DecomposeIrrep[#,ProductAlgebra[SU2,U1],2]]&@ProductIrrep[Irrep[SU5][24],Irrep[SU3][3],Irrep[U1][-3]]
Out[2]=
(24,3)(-3)(24,2)(1)(-3)+(24,1)(-2)(-3)
Applications
(1)
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