Quantum Extremism: Effective Potential and Extremal Paths
arXiv:0907.1174 · doi:10.1140/epjc/s10052-009-1179-8
Abstract
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.
11 pages, 4 figures