Unitarity and locality on patgh integrals

[melthengylf]

my question is this: you know than in feynman path integra, you integrate e^iS/hbar along all the fields. you also know that S is real and that it is the integral of local functions (fields and derivatives of fields). you also know that path integral generates an unitary and local theory. the question is, it generates a local theory because the action is an integral of local functions? it generates unitary theory because the exponent involved is purely imaginary? if not, are these facts anyhow related?? thank you very much. I'm sorry for the untidiness.

 

[atyy]

In Euclidean path integrals, unitarity is related to a condition called "reflection positivity".

http://ncatlab.org/nlab/show/Osterwalder-Schrader+theorem (rigourous QFT)
http://arxiv.org/abs/1005.3751v3 (lattice theory)

There are several sets of conditions that allow one to rigourously recover a relativistic local QFT from Euclidean path integrals. One set are the Osterwalder-Schrader conditions, which are discussed in http://www.rivasseau.com/resources/book.pdf (p17)

 

[melthengylf]

that's both excellent answers! I'm reading about it now. I'm really grateful.