Hi, my name is Moises Zeleny, I am from Mexico, and I am studyng a PhD on
applied physics, particularly I am working on Model building in particle
physics, I am a begginer in sympy programming but I think sympy is very
useful for physics calculation. I would like to build my own python program
to do a similar things like feynarts and feynrules in Mathematica. My first
step, I have been using sympy to do all algebra manipulations to reproduce
the Standard Model of particles physics and some its extensions. But I want
to go to the next level. For example, with sympy symbols I can find all
posible vertices (interactions) in my Lagrangian, and my program give me a
list :
interactions_list = [[h,f,fb],[h,W,W],[h,Z,Z],[h,gamma,gamma],[Z,f,fb]
,[gamma,f,fb],[Z,f,fb]]
Then with the sublist [h,W,W], [h,f,f], ... I can construct some feynman
diagrams permited in my Lagrangian. For example I can construct all allowed
2 ->1 ->2 process using the next class
class Vertice3(Expr):
def __init__(self,x1,x2,x3):
self.x1 = x1
self.x2 = x2
self.x3 = x3
def __str__(self):
return '{a}{b}{c}'.format(a=latex(self.x1), b=latex(self.x2),\
c=latex(self.x3))
def __repr__(self):
return self.__str__()
def __eq__(self,other):
q1,q2,q3 = self.x1,self.x2,self.x3
k1,k2,k3 = other.x1,other.x2,other.x3
return (q1==k1 and q2==k2 and q3==k3) or (q1==k2 and q2==k3 and
q3==k1) or (q1==k3 and q2==k1 and q3==k2) \
or (q1==k1 and q2==k3 and q3==k2) or (q1==k2 and q2==k2 and
q3==k3) or (q1==k3 and q2==k2 and q3==k3)
# definimos como va a funcionar el operador in para la clase Vertice3
def __contains__(self,obj):
return obj==self.x1 or obj==self.x2 or obj==self.x3
##########################################
and the function:
#########################################
def diagramas121(p1,p2,interacciones):
pi = p1 # initial particles
pf = p2 # final particles
propagadores = []
diagramas = []
vertices = [Vertice3(*inte) for inte in interacciones]
for vertex in vertices:
if pi in vertex:
if pi==vertex.x1:
propagadores.append([vertex.x2,vertex.x3])
elif pi==vertex.x2:
propagadores.append([vertex.x1,vertex.x3])
else:
propagadores.append([vertex.x1,vertex.x2])
for vertex in vertices:
for prop in propagadores:
if (prop[0]==vertex.x1 and prop[1]==vertex.x2 and
pf==vertex.x3) or\
(prop[0]==vertex.x2 and prop[1]==vertex.x3 and pf==vertex.x1)
or\
(prop[0]==vertex.x3 and prop[1]==vertex.x1 and pf==vertex.x2)
or\
(prop[0]==vertex.x2 and prop[1]==vertex.x1 and pf==vertex.x3)
or\
(prop[0]==vertex.x1 and prop[1]==vertex.x3 and pf==vertex.x2)
or\
(prop[0]==vertex.x3 and prop[1]==vertex.x2 and
pf==vertex.x1):
diagramas.append([pi,prop,pf])
propagadores.remove(prop)
return diagramas
for example with the next code:
##########
h,W,f,fb,gamma,Z = symbols(r'h,W,f,\overline{f},\gamma,Z')
interactions_list = [[h,f,fb],[h,W,W],[h,Z,Z],[h,gamma,gamma],[Z,f,fb]
,[gamma,f,fb],[Z,f,fb]]
diagramas212([f,fb],[f,fb],interactions_list)
##########333
The I obteind the next list:
[[f,fb,[h],[f,fb]], [f,fb,[Z],[f,fb]],[f,fb,[gamma],[f,fb]]]
I would like to give some properties of each symbols (particle), like four
momentum or the corresponding Dirac Spinor (at the fermion case (f)) or
propagator for h and f. Then calculate for example the amplitude for each
process. I have thought in a structure like this:
M = fb.spinor()*ghff*f.spinor()*h.propagator()*fb.spinor()*ghff*f.spinor()
where ghff represent the coupling constant between h and f , fb which I can
calculate with sympy. Can someone give me some suggestions for do it?
Thanks in advance and I am sorry for my grammar.
[[f,f⎯⎯⎯,[h],f,f⎯⎯⎯],[f,f⎯⎯⎯,[Z],f,f⎯⎯⎯],[f,f⎯⎯⎯,[γ],f,f⎯⎯⎯]][[f,f⎯⎯⎯,[h],f,
f⎯⎯⎯],[f,f⎯⎯⎯,[Z],f,f⎯⎯⎯],[f,f⎯⎯⎯,[γ],f,f⎯⎯⎯]]
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