Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
GSberveglieri`Phi4tools`
XCubicRatio  | |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
Needs["GSberveglieri`Phi4tools`"]
Let's look at the diagram for for the theory with =3 quartic vertices, let's visualize it and print its symmetry factor for the theory with O(N) model broken to cubic symmetry:
nd
2
(2)
Γ
4
ϕ
v4
In[2]:=
[2,0,3,1],
[2,0,3,1,"Tensor""Cubic"]
 | VisualizeDiagram |
| SymmetryFactorDiagram |
Out[2]=
,+++2Χ+ΝΧ+++
4
9
4Ν
9
2
Ν
9
8
2
Χ
3
Ν
2
Χ
3
3
Χ
Using the function with the option "Tensor"->"Cubic" is possible to get both these information at the same time, for example
In[3]:=
info4031=
[4,0,3,1,"Tensor""Cubic"]
 | InformationDiagram |
Out[3]=
| |||||||||||||||||
In[4]:=
info4031["Symmetry Factor"]
Out[4]=
| |||||
The four coefficients are those for the three channels of the 4-pt functions of the O(N) model and for the tensorial structure of the anisotropic term, respectively.
The actual contribution for a given Feynman diagram is given by the product between the value of the diagram and symmetry factor that can be printed with and , respectively. For example at the order for for the cubic model we have
4
λ
(2)
Γ
In[5]:=
FullSimplify
[2,0,4].
[2,0,4,"Tensor""Cubic"]
| ValueDiagram |
| SymmetryFactorDiagram |
Out[5]=
1
243
±
1.9×
)+Ν((2119.89727713855838649-16
10
±
1.0×
)+Ν((461.771717162301630254-16
10
±
2.1×
-17
10
±
3.0×
)Ν))+((15567.2455636642092064-25
10
±
1.1×
)+Ν((4935.76088099924571576-15
10
±
2.5×
-16
10
±
4.×
)Ν))Χ+(28245.5600949787509341-24
10
±
2.0×
)+Ν(2983.78747494424006137-15
10
±
8.×
)-72Log-17
10
4
3
2
Χ
±
1.4×
)+54-15
10
2
π
4
3
3
Χ
±
3.4×
)-16
10
4
Χ
 |
|
 |
|
 |
|
""