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" There are close analogies between quantum field theories in d dimensions and classical statistical mechanics in d + 1."

What does this statement imply and from where does this extra dimension come from? Is it because we introduce imaginary time, $t = -i\tau$ ?

Qmechanic
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Draco_1125
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  • If the statement is talking about Wick rotation, then probably it's because classical statistical mechanics, being the study of equilibria, is not time-dependent (i.e. time doesn't really appear as a variable), so you need an extra spatial dimension to capture the full dimensionality of a quantum system. – probably_someone Jan 27 '18 at 06:10
  • Related: https://physics.stackexchange.com/q/87306/2451 and links therein. – Qmechanic Jan 27 '18 at 10:06
  • Where does this quote come from? – valerio Feb 04 '18 at 08:12
  • Chap 3 Atland and Simon's field theory – Draco_1125 Feb 04 '18 at 09:11

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