Monday, February 28, 2005
How to Put an End to the Suffering Caused by Path Integrals
Path integrals have caused a lot of suffering amongst theoretical physicists. Lubos Motl gives a nice summary about Wick-rotation used quite generally as a trick to give some meaning to these poorly defined objects which have caused so much frustration. The idea of Wick rotation is to define path integrals of quantum field theory in Minkowskian space M^4 by replacing M^4 temporarily by Euclidian space E^4, by calculating the integral here as Euclidian functional integral having more meaning, and returning back to M^4 by analytically continuing in various parameters such as the momenta of particles. The trick has been also applied in the hope of making sense of path integral of General Relativity as well as in string models. I have never liked the trick, not because it is a trick, but just for the fact that this trick is needed at all. Something must be fatally wrong at the fundamental level. To see what this something might be, one must recall what Feynman did for long time ago.