Talk:Wick rotation

QFT

how does such an analytic continuation relate stat mech to qft? does anyone know?

thank-you!

70.27.140.234 19:59, 26 Apr 2005 (UTC)

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The relationship between QFT and statistical mechanics arises because after Wick rotation the 4-space has a Euclidean metric, just like the three space in problems in statistical mechanics. Therefore oftentimes expressions from QFT are formally identical to those in statistics. This has nothing to do with the spin-statistics theorem.

TobiS 12:05, 2005 Jun 21 (UTC)

Would it be worth mentioning that neither the Minkowsi metric is a metric but rather a pseudometric nor that the resulting formula does comply, in a strict sense, with any norm on the complex vector space and thus any theorem valid for a metric or norm cannot be used whitout checking if it is still valid in this deviated case. 84.160.211.96 10:20, 7 January 2006 (UTC)[reply]

Explain

It would help if this article actually had an English language explanation. —Preceding unsigned comment added by Wildspell (talk • contribs) 07:17, 21 April 2009 (UTC)[reply]

It would be great if physicists understood this well enough that such an explanation were possible! Someday that may happen, but right now Wick rotation is somewhere between a "trick" and a "deep mystery". John Baez (talk) 12:57, 5 August 2024 (UTC)[reply]

No rotation

The use of a pure imaginary variable to relate the pseudo-Euclidean with the Euclidean is an old ploy in mathematical physics. It does not contribute to insight. Readers should review hyperbolic angle to grow beyond the Euclidean concept of angle. Note particularly the section hyperbolic angle#Imaginary circular angle where a similar ploy is exposed.Rgdboer (talk) 21:44, 7 October 2011 (UTC)[reply]

Polemical. 178.38.132.48 (talk) 19:39, 14 May 2017 (UTC)[reply]

In 1908 Felix Klein considered a mapping equivalent to the Wick rotation in the context of the complex projective plane and called it "imaginary transformation". He analyzed the significance of this geometric algebra for the circular points at infinity that lie on any circle in that plane. While physics authors accept this mapping as appropriate, Klein notes the geometric consequences. The statement in this article that the mapping is a 90° rotation, closer examination shows that the matter is not that simple, in fact it distorts the underlying geometry.— Rgdboer (talk) 20:45, 24 September 2024 (UTC)[reply]

Connection with Minkowski space

I can't see a connection in examples with Minkowski space, because there is no relativistic invariance in there models => they have nothing to do with Minkowski space. Seems that Wick rotation does not rely on the metrics. Or the examples are incorrect. Sorry for my English 109.252.154.222 (talk) 15:54, 10 January 2013 (UTC)[reply]

Complex variables are used in biquaternions to obtain the Minkowski metric.Rgdboer (talk) 04:02, 10 January 2022 (UTC)[reply]

Hawking referring to "imaginary time"

There is a "citation needed" after the line

When Stephen Hawking wrote about "imaginary time" in his famous book A Brief History of Time, he was referring to Wick rotation.

I can't see why one would need a "citation" for that. Of course he's talking about the Wick rotated time. One might as well demand a citation showing that when Stephen Hawking talks about "imaginary numbers", he is referring to numbers in C ... Or one can point people to Euclidean quantum gravity, which is what Hawking was working on. 2001:7E8:C07E:3E01:223:54FF:FE15:1831 (talk) 12:13, 2 February 2013 (UTC)[reply]

A good reference would point to the pages where Hawking discusses this, so readers can consult those. But his book with Penrose would also be a useful citation: more accessible than a research paper, but much more detailed than A Brief History of Time.

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