# 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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### Regularization of loop integrals with Feynman slash

As the title suggests, I am trying to compute a loop integral with a Feynman slash in the numerator, like $$\int\frac{d^Dq}{(2\pi)^D}\cdot\frac{q_\mu\gamma^\mu}{\left(q^2+\Delta+i\epsilon\right)^3}$$ ...
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### Is there ever a situation where statistical electrodynamics is needed?

I.e. compute the Euclidean path integrals of QED/the statistical field theory of electrodynamics? I have never seen anyone discuss this anywhere and I am wondering why? What if there is just an ...
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### Euclidean Black hole diagram

I am trying to understand how the Euclidean "cigar" is built. I understand how and why the time is periodic, as for the radius of the cigar I am confused, it should be constant far from the ...
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### Is the Euclidean generating functional $Z_{E}[J]$ identified with original Minkowskian generating functional $Z[J]$?

In quantum field theory, it is common to perform wick rotation $t\rightarrow -i\tau$ and get Euclidean generating functional $Z_{E}[J]$. When I first studied QFT, I just saw this a magic trick to ...
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### Taking imaginary time to show damping relation in path integral formalism

I'm having trouble with a step in the reasoning in pg.9 of Bailin & Love - Introduction to gauge field theory: To find the ground-state to ground-state amplitude we have a term:(given a basis of ...
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### Radial quantization and time order

In CFT, one ususally begins quantization by defining radial ordering on the complex plane, with the notion of radial ordering being the equivalence of time ordering. This is often "motivated"...
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### How are Schwinger and Wightman functions used in practice?

In Reed & Simon's Methods of Mathematical Physics Volume II, they define a (Hermitian scalar) quantum field theory to be the quadruple $\langle \mathcal{H}, U, \varphi, D\rangle$ that satisfies ...
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### Why do we call it "Euclidean Quantum Gravity" instead of "Riemannian Quantum Gravity"?

Euclidean quantum gravity is an approach to quantum gravity based on working with Riemannian-signature manifolds and eventually relating the results to our Lorentzian spacetime by means of analytic ...
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### Euclidean Time Feynman Path Integral as Stochastic Differential Equation

For a quantum system with Lagrangian $L(x, \frac{dx}{dt})$ we can represent the action of a path $\mathbf{x}$ as $$S(\mathbf{x}) = \int_0^{t} L(\mathbf{x}(s), \mathbf{\frac{dx}{dt}}(s)) ds.$$ Then, ...
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### Performing Wick rotation under conjugation

See the formulas (95) and (96) of this notes https://arxiv.org/abs/1602.07982. When one try to perform the Wick rotation $t=-i\tau$ to the field in Minkowski/Lorentzian spacetime \mathcal{O}_L(t, \...
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### Hawking temperature for an asymptotically $\text{AdS}_5$ black hole with a constant magnetic field

I'm trying to calculate the Hawking temperature for an asymptotically $\text{AdS}_5$ black hole with a constant magnetic field. Suppose that the metric and magnetic field of this background are given ...
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### What would be the problems with supposing spacetime to be fundamentally Riemannian, not Lorentzian?

I'm thinking about the Wick rotation. My question may be similar to this one but I don't think it's a duplicate, though you can judge that. Suppose we take the Wick rotation as an indication that ...
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### Wick rotation in Peskin and Schroeder's QFT

I know there are many similar analysis about this topic, like here, here, many of them are answered by Qmechanic, excellent answer! I have checked most of these posts, but I still don't clearly ...
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### Green Function in Euclidean space time

My question based on Ashok Das's "Finite Temperature Field Theory", page 12-13. The book assume that in bosonic Klein-Gordon theory, zero temperature Green function satisfies (metric in ...
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### Can the QFT path integral be re-expressed using a real, positive-definite function of the action? [duplicate]

This question is based on my rather shaky grasp of QFT, so if I'm missing a key concept then just let me know! If you're deriving the Schrodinger equation from the path integral as Feynman did, then ...
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### Continuum limit of lattice field theory

Just a simple question for lattice QCD experts, is continuum limit of lattice field theory a relativistic quantum field theory? Because i heard that lattice QCD is done in imaginary time, producing a ...
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