Quantum Extremism: Effective Potential and Extremal Paths

Understand

The reality and convexity of the effective potential in quantum field theories has been studied extensively in the context of Euclidean space-time.

• It has been shown that canonical and path-integral approaches may yield different results, thus resolving the `convexity problem'.
• We discuss the transferral of these treatments to Minkowskian space-time, which also necessitates a careful discussion of precisely which field configurations give the dominant contributions to the path integral.
• In particular, we study the effective potential for the N=1 linear sigma model.