Recent content by JRudolfo

Thanks everyone. Just a quick note - it seems in particle physics you use the counter-term formalism, so that the Lagrangian splits into a renormalized part plus a counter-term part. The renormalized parameters are chosen so that the classical solution to the renormalized Lagrangian is the...

So would you say this is correct to 2nd order: $$\int d\phi \, e^{iS[\phi]} \phi=\int d\phi \, e^{iS[\phi_c]+i/2 S^{(2)}[\phi_c](\phi-\phi_c)^2} \phi=\int d\phi\, e^{iS[\phi_c]+i/2 S^{(2)}[\phi_c](\phi)^2}(\phi_c+\phi)=\phi_c$$ where we used oddness of integrand and translational shift...

Hi, I think it's simpler to think of a single random variable X with probabality distribution P(x), so if you want the expectation value of X, it's given by: $$\langle X \rangle =\int \,dx P(x) x$$ To make the analogy with quantum mechanics, X would be \phi(x), and P(x) would be the...

A scalar field theory with potential $$V(\phi)=-\mu^2\phi^2+\lambda \phi^4$$ is spontaneously broken and as a consequence, for the ground state, $$\langle \phi(x) \rangle \neq 0$$. However, the path integral, which should give ground state expectation values, looks to be zero by oddness of the...