nLab complex path integral

The action functional is real valued. Path integral is defined for such real action functionals. The Wiener integral is an analogue which is well defined in statistics and which is like an analogue for imaginary values of action functional.

Recently, some considerations were given to general complex valued functional arising from the analytic continuation of the real case. This research is related to the study of the wall crossing, Stokes phenomenon for path integrals, to the complex Chern-Simons theory? and so on.

• Edward Witten, Analytic continuation of Chern–Simons theory, arXiv:1001.2933; A new look at the path integral of quantum mechanics, arXiv:1009.6032; D. Harlow, J. Maltz, E. Witten, Analytic continuation of Liouville theory, arxiv/1108.4417
• D. D. Ferrante, G. S. Guralnik, Z. Guralnik, C. Pehlevan, Complex path integrals and the space of theories, arxiv/1301.4233 (note a very good bibliography there)