HOW EFFECTIVE IS THE EFFECTIVE POTENTIAL

Motivated by bubble nucleation in first order phase transitions, we qu estion the validity of the effective potential for inhomogeneous confi gurations. In an attempt to get some insight into the importance of de rivative terms, we analyze a simple model, a kink in 1 + 1 dimensions and zero temperature. We evaluate the energy shift from the quantum fl uctuations about the non-uniform background (i.e. the effective action ) and compare it to the energy from the effective potential. Our resul ts clearly show that for inhomogeneous configurations it may be inadeq uate to omit derivative terms and confine oneself to the effective pot ential. We then couple the kink field to an additional scalar field an d perform the same comparison. The addition of the second field allows us to vary the mass of the fluctuations and their coupling to the und erlying kink. If the mass of the second field is large, it does not fe el the inhomogeneities in the kink field and consequently does not giv e rise to important derivative corrections in the effective action. In contrast, if the mass is small, derivative terms are significant and the effective potential fails. In the latter regime we can, however, r ely on the Born approximation to calculate the effective action.