# Why do Feynman rules work?

Gold Member
I am reading Peskin and Schroeder and finished a few years ago Srednicki.

What I don't understand is why do Feynman rules work?

They are supposed to represent the diverging integrals that appear in the calculations, i.e momentum integrals, are they supposed to be regarded as a pictorial description of the collisions in the experiments?

Beside a way to write the diverging integrals, do they have other meanings?

The deformations we introduce can be written as a point-dependent unitary transformation ##\hat\xi(x)=\hat U^{-1}(x)\hat\phi(x)\hat U(x)##, where ##\hat\phi(x)## is a free quantum field and ##\hat U(x)## is the time-ordered exponential $$\hat U(x)=\mathrm{T}\left[\mathrm{e}^{-\mathrm{i}\int\limits_{y\preceq x} \hat H_\mathrm{int}(y)\mathrm{d}^4y}\right].$$ The integral is over all points ##y\preceq x## that causally precede ##x##, which deforms the Hamiltonian density of the free field, ##\hat H_0(x)\mapsto\hat H_0(x)+\hat H_\mathrm{int}(y)##. If we work formally, ignoring niceties of whether ##\hat H_\mathrm{int}(y)## exists and whether the integral exists, expansions include integrals that can be pictorially presented as Feynman diagrams.