Seminarium Teorii Oddziaływań Elementarnych

Stochastc quantization is a well known approach which replaces ensamble averages by averaging over a fictitious time of a suitable stochastic process. It was designed and proved for positive densities, i.e. real, euclidean actions. However Langevin process can be also defined for complex actions, raising expectations for statistical averaging over complex distributions. This has attracted a new wave of interest after recent reports of successful study of quantum chromodynamics at finite chemical potential. Nevertheless there is no proof of convergence in the complex case, and indeed the evidence for success is limited.
In this talk we will circumvent above problems by introducing additional variables and direct construction of corresponding (i.e. complex and positive) weights. As an application, the well known solution for a complex gaussian distribution will be generalized to arbitrary complex inverse dispersion parameter. This opens a way to construct positive representations of path integrals directly in Minkowski time as will be done in the second part of the talk. Then some applications to simple, classic quantum systems will be presented.
Finally a striking physical interpretation of the new structure will be suggested, albeit with due caution.