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Questions tagged [wick-rotation]

Wick rotation substitutes an imaginary-number variable for a real-number time variable to map an expression or a problem in Minkowski space to one in Euclidean space which are easier to evaluate or solve. Use for all types of rigid analytic continuation maps.

Wick rotation substitutes an imaginary-number variable for a real-number time variable to map an expression or a problem in Minkowski space to one in Euclidean space which are easier to evaluate or solve. The well-definition of the Lorentzian depends on interpreting it as a Wick rotation of an Euclidean path integral.

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How exact is the analogy between statistical mechanics and quantum field theory?

Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a few questions about the relation between the two…
user26866
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Wick rotation in field theory - rigorous justification?

What is the rigorous justification of Wick rotation in QFT? I'm aware that it is very useful when calculating loop integrals and one can very easily justify it there. However, I haven't seen a convincing proof that it can be done at the level of…
user17116
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The meaning of imaginary time

What is imaginary (or complex) time? I was reading about Hawking's wave function of the universe and this topic came up. If imaginary mass and similar imaginary quantities do not make sense in physics, why should imaginary (or complex) time make…
glebovg
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Euclidean derivation of the black hole temperature; conical singularities

I am studying the derivation of the black hole temperature by means of the Euclidean approach, i.e. by Wick rotating, compactifying the Euclidean time and identifying the period with the inverse temperature. Consider the Schwarzschild case as an…
ScroogeMcDuck
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Gaussian integral with imaginary coefficients and Wick rotation

Although this question is going to seem completely trivial to anyone with any exposure to path integrals, I'm looking to answer this precisely and haven't been able to find any materials after looking for about 40 minutes, which leads me to believe…
Adomas Baliuka
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Reflection positivity for general fields

In the Euclidean QFT obtained by "Wick-rotating" a unitary QFT, the correlation functions satisfy a property called reflection positivity, see e.g. this Wikipedia article for the case of a scalar field. What's the correct formulation if you have…
Yuji
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Wick rotation and spinors

I am quite familiar with use of Wick rotations in QFT, but one thing annoys me: let's say we perform it for treating more conveniently (ie. making converge) a functional integral containing spinors; when we perform this Wick rotation, in a way we…
toot
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Subtlety of analytic continuation - Euclidean / Minkowski path integral

I subconsciously feel not fully comfortable about Wick rotating or analytic continuation from Euclidean to Minkowski space. I simply wonder whether there is any subtlety here, and when we need to be conscious whether (i) this continuation can be…
wonderich
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What is a simple intuitive way to see the relation between imaginary time (periodic) and temperature relation?

I guess I never had a proper physical intuition on, for example, the "KMS condition". I have an undergraduate student who studies calculation of Hawking temperature using the Euclidean path integral technique, and shamefully his teacher is not able…
Demian Cho
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How to Perform Wick Rotation in the Lagrangian of a Gauge Theory (like QCD)?

I'm studying Lattice QCD and got stuck in understanding the process of going from a Minkowski space-time to an Euclidean space-time. My procedure is the following: I considered the Wick rotation in quantum mechanics $x_0 \to -i x_4$. From this, I…
WilhelmM
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Connection between Schrödinger equation and heat equation

If we do the wick rotation such that τ = it, then Schrödinger equation, say of a free particle, does have the same form of heat equation. However, it is clear that it admits the wave solution so it is sensible to call it a wave equation. Whether we…
Kevin Kwok
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LSZ reduction vs adiabatic hypothesis in perturbative calculation of interacting fields

As far as I know, there are two ways of constructing the computational rules in perturbative field theory. The first one (in Mandl and Shaw's QFT book) is to pretend in and out states as free states, then calculating $$\left\langle i \left| T…
user26143
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Problems while Wick rotating the path integral

I am trying to begin from the path integral of QM and write the Euclidean version of it performing the Wick rotation but it seems that I am missing a few things. For simplicity I work on 1 dimension and in natural units. The amplitude for a spinless…
Yossarian
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Minkowski Metric Signature

When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ ds^{2} = -(c^{2}dx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2} $$ where $ x^0,x^1,x^2,x^3 $ come from $ x^{\mu} : \mu…
Doryan Miller
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Quantum field theory: zero vs. finite temperature

I have recently been made aware of the concept of thermal field theory, in which the introductory statement for its motivation is that "ordinary" quantum field theory (QFT) is formulated at zero temperature. Now, I have read through the introductory…
Will
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