GSberveglieri/Phi4tools | Paclet Repository

GSberveglieri`Phi4tools`

NComponents

NComponents []
	represents the number Ν of field components.

Details and Options



Examples

(1)

Basic Examples

(1)

In[1]:=

Needs["GSberveglieri`Phi4tools`"]

Let's look at the

diagram for

(2)

for the

theory with

=3 quartic vertices, let's visualize it and print its symmetry factor for the

O(Ν)

model:

In[2]:=



VisualizeDiagram

[2,0,3,1],

SymmetryFactorDiagram

[2,0,3,1]

Out[2]=



4Ν



Using the function

InformationDiagram

with the option "Tensor"->"O(N)" is possible to get both these information at the same time, for example

In[3]:=

InformationDiagram

[4,0,3,1,"Tensor""O(N)"]

Out[3]=

External Legs	4
Cubic Vertices	0
Quartic Vertices	3
List Number	1
Nickel Index	ee11\|22\|ee\|
Symmetry Factor	 4 9 + 2GSberveglieri`Phi4tools`NComponents[] 9 + 2 GSberveglieri`Phi4tools`NComponents[] 27 , 4 27 , 4 27 
Diagram
Value	1

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

ValueDiagram

and

SymmetryFactorDiagram

, respectively. For example at the order

for

(2)

In[4]:=

Simplify

ValueDiagram

[2,0,4].

SymmetryFactorDiagram

[2,0,4]

Out[4]=

(10.6771231575200337492

8.×

-19

)+Ν((8.72385710756608389503

6.×

-19

)+Ν((1.90029513235515074179

9.×

-20

)+(0.1038236839760586157907245574

1.2×

-27

)Ν))

We could also look at the theory with O(N) model broken to cubic symmetry with the option "Tensor"->"Cubic", for example

In[5]:=

InformationDiagram

[2,0,4,3,"Tensor""Cubic"]

Out[5]=

Failure



Reason: Invalid signature in CloudSystem`Signing`SignedExpression[DynamicModule[{Set[TypeSystem`NestedGrid`PackagePrivate`renderedGrid,Deploy[Style[Grid[{{Item[Pane[Annotation[EventHandler[MouseAppearance[Mouseover["External Legs",Style["External 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