Complex path -- a semi-classical probe of quantum effects

I will discuss the notion of an effective, average, quantum mechanical path which is a solution of the dynamical equations obtained by extremizing the quantum effective action. Since the effective action can, in general, be complex, the effective path will also, in general, be complex. The imaginary part of the effective action is known to be related to the probability of particle creation by an external source and hence one expects the imaginary part of the effective path also to contain information about particle creation. We can identify such features using simple examples including that of effective path through the black hole horizon leading to thermal radiation.