# 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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### Strange Wick rotation in the computation of string partition function

In order to compute the one-loop vacuum-to-vacuum amplitude for the bosonic string, one runs into \begin{equation} Z(\tau) = V_D (q \bar{q})^{-D/24} \int \frac{d^Dk}{(2 \pi)^D} \exp({- \pi \alpha^\...
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### Temperature of quantum fields and periodicity

I have read this PSE post Finite Temperature Quantum Field Theory, saying that In a QFT at finite temperature, we consider the Euclidean time to be periodic, i.e. we consider a theory on the manifold ...
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### Why do we Wick rotate before regularizing Feynman diagrams?

In Folland's Quantum Field Theory he mentions that we can apply Feynman's formula (Feynman parameterization) to either the Wick rotated integrals or the non-Wick rotated integrals corresponding to ...
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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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### Imaginary velocity components in geodesic [duplicate]

When we try to find the geodesic of a partical at rest, in the second term of the geodesic equation we use dt/dtau = 1. Shouldn’t it be i (for imaginary number), since the time component of the 4-...
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### Hamiltonian and Lagrangian for a particle on a ring [duplicate]

In the book Condensed Matter Field Theory (A. Altland & B. Simons)(page 498, 2nd edition) they suggest the following Hamiltonian and Lagrangian for a particle on a ring in the presence of a ...
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### Why does the Lagrangian have $O(4)$ symmetry after Wick rotating (previously Lorentz symmetry)?

Pertaining to the answer within link. Why is it the case, that for Lorentz invariant Lagrangian $\mathcal{L}$, after Wick rotation, the $O(4)$ invariance is established, thus manifesting itself as ...
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### Wick rotation of contravariant vector field holomorphic?

Suppose one has a contra variant vector field in Minkowski spacetime $A^\mu : \mathbb{R}^{1+3} \to \mathbb{R}$ for each component $\mu$ inside some path integral. I assume, that one can analytically ...
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### Physics in Euclidean spacetime [duplicate]

I just have a very small and naive Question. In my PhD I work on different Toy models which are implemented on the lattice. In order to do so one performs a Wick rotation from minkowski to euclidean ...
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### On symmetry of Lorentz matrix

For Lorentz transformations, if we put $x^1=x$ and $x^2=ct$ and restrict ourselves to $2D$ we get $$x'=\gamma(x-\beta ct) \tag{1}$$ $$ct'=\gamma(ct-\beta x) \tag{2}$$ The matrix associated with this ...
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### Chiral symmetry of the Euclidean action for fermions

In the literature, such as QFT Volume-II by Weinberg, p.368, the chiral anomaly is derived using Euclidean path integral. To formulate the question, let's start with the Minkowski space with signature ...
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### Is the Schrödinger equation the heat equation with imaginary constants?

Playing around with the Schrödinger equation, I separated the time partial derivative this way: \frac{\partial \Psi}{\partial t}=\frac{i\hbar}{2m}\frac{\partial^2\Psi}{\partial x^2}-\frac{i}{\hbar}V\...
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### Is the value of the action important?

I know that the action, in Classical Mechanics, is a functional of the path of a physical system, such that "the path actually followed by a physical system is that for which the action is ...
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Given a (non-relativistic) propagator $K_t(A,B)$ giving the 'conditional amplitude' to go from state $B$ to state $A$ in time $t$, it is known that one can find the vacuum wavfunction by (independent ... The Wick's rotation $W$ facilitates dealing with integrals in the Minkowski space by rotating time into the Euclidean space. As this rotation in time is performed within integrals, one can view that ...