# Expansion around a classical vacuum

by GargleBlast42
Tags: classical, expansion, vacuum
 P: 28 Hi everyone, I have a severe confusion about the notions of "expanding the theory around a classical vacuum" and "considering small fluctuations around a classical vacuum" which I find in QFT textbooks. My problem is: in the path integral $$\int D\phi e^{i S[\phi]}$$ one doesn't integrate only over field configurations close to the vacuum, but over all field configurations. And when one is considering a perturbative expansion, this expansion is in the coupling constant (like $$\lambda$$ in $$\phi^4$$ theory), but one doesn't assume $$\phi$$ to be small, or am I wrong? So the questions would be: Why does one require the field configurations to be small fluctuations around a classical vacuum? And what would happen if I was expanding the theory about a field configuration that is not a classical vacuum (except that the mass could be possibly negative)? The first question is more important for me. I would be very grateful for any clarification.