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Phi4tools

Guides

  • Phi4tools

Tech Notes

  • Feynman Diagram Evaluation
  • Perturbative Series Generation

Symbols

  • BubbleSubdiagram
  • CountLoops
  • DeriveAndWriteExplicit
  • DrawGraph
  • ExternalMomentum
  • InformationDiagram
  • IntegrandDiagram
  • Momentum
  • MomVars
  • NComponents
  • NickelIndex
  • Propagator
  • SquareSubdiagram
  • SunsetSubdiagram
  • SymmetryFactorDiagram
  • TadSunsetSubdiagram
  • TadTriangleBubblesSubdiagram
  • TriangleSubdiagram
  • ValueDiagram
  • VisualizeDiagram
  • WriteExplicit
  • XCubicRatio
GSberveglieri`Phi4tools`
SymmetryFactorDiagram
​
​
SymmetryFactorDiagram
[n,v3,v4,d]
gives the tensorial symmetry factor for the
d
-th diagram of the
n
-point function with
v3
cubic vertices and
v4
quartic vertices.
​
​
SymmetryFactorDiagram
[n,v3,v4]
gives the list of tensorial symmetry factors for the diagrams of the
n
-point function with
v3
cubic vertices and
v4
quartic vertices.
​
Details and Options

Examples  
(2)
Basic Examples  
(1)
In[1]:=
Needs["GSberveglieri`Phi4tools`"]
Symmetry factor for the
th
60
Feynman diagram for
(2)
Γ
for the O(N) model at the order
6
λ
.
In[2]:=
SymmetryFactorDiagram
[2,0,6,60]
Out[2]=
272
729
+
296Ν
729
+
128
2
Ν
729
+
10
3
Ν
243
+
4
Ν
243
Symmetry factors for
(4)
Γ
for the O(N) model at the order
4
λ
.
TableForm
allows to better appreciate the structure of the output.
In[3]:=
SymmetryFactorDiagram
[4,0,4,"Tensor""O(N)"]​​TableForm@%
Out[3]=

32
81
+
8Ν
27
+
8
2
Ν
81
+
3
Ν
81
,
8
81
,
8
81
,
32
81
+
2Ν
9
+
2
Ν
27
,
4
27
+
2Ν
81
,
4
27
+
2Ν
81
,
8
27
+
2Ν
9
+
2
Ν
27
,
4
27
+
2Ν
27
,
4
27
+
2Ν
27
,
28
81
+
4Ν
27
+
2
Ν
81
,
16
81
+
4Ν
81
,
16
81
+
4Ν
81
,
8
27
+
10Ν
81
+
2
Ν
81
,
16
81
+
2Ν
27
+
2
Ν
81
,
16
81
+
2Ν
27
+
2
Ν
81
,
32
81
+
2Ν
9
+
2
Ν
27
,
4
27
+
2Ν
81
,
4
27
+
2Ν
81
,
16
81
+
4Ν
81
,
20
81
+
8Ν
81
+
2
Ν
81
,
8
27
+
8Ν
81
,
22
81
+
5Ν
81
,
22
81
+
5Ν
81
,
22
81
+
5Ν
81

Out[3]//TableForm=
32
81
+
8Ν
27
+
8
2
Ν
81
+
3
Ν
81
8
81
8
81
32
81
+
2Ν
9
+
2
Ν
27
4
27
+
2Ν
81
4
27
+
2Ν
81
8
27
+
2Ν
9
+
2
Ν
27
4
27
+
2Ν
27
4
27
+
2Ν
27
28
81
+
4Ν
27
+
2
Ν
81
16
81
+
4Ν
81
16
81
+
4Ν
81
8
27
+
10Ν
81
+
2
Ν
81
16
81
+
2Ν
27
+
2
Ν
81
16
81
+
2Ν
27
+
2
Ν
81
32
81
+
2Ν
9
+
2
Ν
27
4
27
+
2Ν
81
4
27
+
2Ν
81
16
81
+
4Ν
81
20
81
+
8Ν
81
+
2
Ν
81
8
27
+
8Ν
81
22
81
+
5Ν
81
22
81
+
5Ν
81
22
81
+
5Ν
81
Options  
(1)

SeeAlso
NickelIndex
 
▪
NComponents
 
▪
XCubicRatio
 
▪
ValueDiagram
 
▪
InformationDiagram
TechNotes
▪
Perturbative Series Generation
RelatedGuides
▪
Phi4tools
""

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