Sunday, June 11, 2017

Comparing interaction potential in standard ϕ4theory


I am posting this question again because, Willie Wong asked me to do it. So it is a continuing post of the Interaction potential in standard ϕ4 theory.


I have been studying about solitions so I had to deal with scalar field theory. The problem I faced in Lagrangian of Scalar field is interacting potential.


According to Scalar field theory we can write: L=12μϕμϕm22ϕ2λ4!ϕ4

The potential can be written separately V(ϕ)=m22ϕ2+λ24ϕ4
I found on Srednicki (Quantum Field Theory, page 188) that, the author wrote the potential as, V(ϕ)=124λ(ϕ2v2)2λ24v4
After that the author excluded the term λ24v4.


why is that?


In another paper an author wrote the potential as V(ϕ)=18ϕ2(ϕ2)2


I don't see coupling constant λ in the equation (4).


What I'm trying to find is to get the potential in equation (4) from the equation (2)




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