Monday, September 11, 2017

quantum field theory - How the nonlinear equation can be written like this?


We consider a scalar theory in a 1+D dimensional flat Minkowski space-time, with a general self-interaction potential, whose action can be written as A=dtdDx[12(tϕ)212(iϕ)2U(ϕ)],

where ϕ is a real scalar field, t=/t, i=/xi and i=1,2,,D. The equation of motion following from (???) is a non-linear wave equation (NLWE) which is given as ϕ,tt+Δϕ=U(ϕ)=ϕ+k=2gkϕk
where Δ=Di=12x2i.
I just want to know the logic, that how they transformed the equation (1)




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