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.
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Path integral at large time
From the path integral of a QFT:
$$Z=\int D\phi e^{-S[\phi]}$$
What is a nice argument to say that when we study the theory at large time $T$, this behaves as:
$$ Z \to e^{-TE_0} $$
where $E_0$ is the ...
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"Mass Shell" Condition on Euclidean Scalar Field
This is a basic qft question. I am looking for the condition on a free scalar $\phi$ of mass $m$ in Euclidean space such that it satisfies the Klein-Gordon equation.
The Euclidean space Klein-Gordon ...
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Motivation behind reflection positivity
I have taken a look at this physicsSE question, Wikipedia, and this paper by Jaffe which go over reflection positivity. While they all nicely explain the definition behind reflection positivity and ...
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When is a Schrodinger equation equivalent to a Fokker-Planck equation?
In chap. 3 in these notes on kinetic theory, Tong shows that the Fokker-Planck operator for a particle undergoing overdamped Langevin dynamics in a potential $V$ is equivalent to a Schrodinger ...
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Wick rotation of Electromagnetic Field Lagrangian [duplicate]
So i will directly to the problem. I am not getting how, when we Wick rotate, the EM action should go to (the correct answer)
$$ S_E = \int -d^4 x\frac{1}{4} F_{\mu \nu} F^{\mu \nu} \underbrace{\...
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How is Wick rotation an analytic continuation?
Wick rotation is formally described by the transformation
$$t \mapsto it.$$
In many place it is stated more rigorously as an analytic continuation into imaginary time. I understand why we do it but ...
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Is the Godel universe Wick rotatable?
Take Wick Rotatability being as the way defined in the article by Helleland:
Wick rotations and real GIT
Is the Gödel universe Wick rotatable according to this definition?
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Examples of Path integral $\neq$ Partition function?
Are there any systems we know of whose partition function is not simply Wick rotation of the path integral? Does anyone know of any examples?
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How do I show that Thermal Field Theory works?
Of course it does work. What I'm asking is:
What is the easiest-to-understand, most direct example that shows that Thermal Field Theory is a predictive theory that actually describes how temperature ...
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Wick rotation of CFT three-point function
Let $\langle O_1\cdots O_n\rangle$ be a Euclidean CFT$_d$ correlation function. I know that we can analytically continue to Lorentzian signature as follows. Let $x_i = (\tau_i,\mathbf{x}_i)\in\mathbb{...
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Wick Rotation vs Sokhotski-Plemeli Method to compute internal loop of Feynman correlators
When computing loop integrals in QFT, one often encounters integrals of the form
$$\int_{-\infty}^\infty\frac{dp^4}{(2\pi)^4}\frac{-i}{p^2+m^2-i\epsilon},$$ where we are in Minkowski space with metric ...
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Confusion about choosing an Euclidean world sheet metric in String Theory path integral
When it comes to construct a well-defined path integral for the Polyakov action in Bosonic String Theory, most authors assume that the world sheet metric $g$ is Riemannian (i.e. it has Euclidean ...
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Visualizing CTC - is it related to a "periodic wick rotation"?
As far as I understand Wick rotation, it means the mathematical transformation $$ ct → jct $$
Where $j$ is imaginary unit. While reading on CTC (closed timelike curves) in the Gödel metric I came ...
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How can we use saddle point approximation for a bounce solution which is not even a strict local minimum of the Euclidean action?
In calculating the false vacuum decay, the main contribution to the imaginary energy part of the Euclidean path integral comes from the bounce solution. And we somehow apply saddle point approximation ...
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Justification for Wick rotation for topological insulator
In Appendix B of the paper (1), the authors compute the second Chern number $C_2$ of a band structure by manipulating the ground- and excited-state projection operators $P_{\text{G}}(\mathbf{k})$ and $...
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