Path integrals and statistical mechanics

From: Doriano Brogioli <>
Date: Fri, 20 Jun 2003 15:57:46 +0200

Hi to everybody. I subscribed to this mailing list yesterday, but I'd
like to pose a question since I think it _must_ be the right place.

Quantum mechanics can be formulated in terms of path integrals (Feinmann
integrals). By substituting the time t with an (Euclidean) immaginary
time i s, that is, a real value s times the imaginary root mean square
of -1, the path integral changes to the Boltzmann distribution, where
the energy is the (classical) energy of a continuum (classical)
mechanical system, at temperature 1/h.

 From this fact, someone claims that quantum world is simply a classical
world, but rotated by pi/2 in the complex plane of t: the real world is
classical, but we see it at the wrong angle. In particular, something
similar happens near the event horizon of a black hole, and it should be
the ultimate origin of Hawking radiation.

I tried to derive this relation, or some kind of this, and I concluded
that it holds only at a formal level. Has anyone any idea about this topic?

Doriano Brogioli
Received on Fri Jun 20 2003 - 09:58:46 PDT

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