The wick-rotation tag has no wiki summary.
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2answers
91 views
Imaginary time in QFT
I'm reading chapter 4 of Introduction to Quantum Field Theory by Peskin & Schroeder. In the $\phi^4$ theory, the authors state that the ground state of the interaction theory $|\Omega\rangle$ can ...
3
votes
1answer
63 views
Volume element $\mathrm{d}^4k =\mathrm{d}k^0 \,|\mathbf{k}|^2\,\mathrm{d}|\mathbf{k}| \,\mathrm{d}(\cos\theta) \,\mathrm{d}\phi$ in Minkowski space?
Suppose we have an integral
$$\int \mathrm{d}^4k \,\ f(k)$$
we want to evaluate and that we're in Minkowski space with some metric $(+,-,-,-)$.
Is it true that: $$\mathrm{d}^4k = \mathrm{d}k^0\ ...
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votes
0answers
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Intuition behind the notion of reflection positivity
I came across Yuji's question. I'm finding it difficult to parse the meaning behind what's said on Wikipedia. Could someone give an explanation of the concept involved? I would also appreciate ...
3
votes
1answer
110 views
Diifference between real time propagation and imaginary time propagation?
Suppose I want to solve Nonlinear Schrodinger equation using imaginary time propagation to get the ground state solution. I choose $t = - i t$, and then solve the equation using split step Crank ...
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votes
2answers
160 views
Imaginary time and string theory
Is imaginary time an extra dimension?
In other words, are time and imaginary time considered two separate dimensions?
If so, does imaginary time appear (as a separate dimension) in string theory (thus ...
3
votes
1answer
216 views
Wick Rotation, interpretation of $\bar{p}^2$ vs the usual $p^2=m^2$
Suppose we use the metric $(+,-,-,-)$ thus the momentum squared is
$p^2 = p_0^2-\vec{p}^2 = m^2>0$
Defining $p_E:=\mathrm{i}\cdot p_0$ and $\bar{p}:=(\,p_E,\vec{p})$ with Euclidean norm ...
2
votes
0answers
50 views
Is Wick rotation invariant under proper conformal transformations?
Is Wick rotation invariant under proper conformal transformations? Why or why not?
Does Wick rotation apply to conformal field theories? $(1-i\epsilon )T$ is not invariant under proper conformal ...
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votes
3answers
446 views
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 ...
2
votes
0answers
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Wick rotation for FRW in quantum gravity
There is no timelike Killing vector for FRW cosmologies. In the path integral formalism, is it possible to Wick rotate for quantum cosmology in quantum gravity? If yes, how? If no, how does one work ...
3
votes
2answers
220 views
Can I use imaginary time propagation for many-body problems?
There are various ways to numerically find the ground state energy and wavefunction of a many-body Hamiltonian. You can diagonalize the Hamiltonian and pick out the lowest eigenstate, or you use ...
6
votes
3answers
377 views
Relation between statistical mechanics and quantum field theory
I was talking with a friend of mine, he is a student of theoretical particle physics, and he told me that lots of his topics have their foundations in statistical mechanics. However I thought that the ...
6
votes
1answer
367 views
Wick rotation and the arrow of time
It is well known that we can switch from a statistical system to a quantum mechanical system by a Wick rotation. Has this rotation some implication on the way the time flow? namely, this is an ...
5
votes
1answer
253 views
Analytic continuation of imaginary time Greens function in the time domain
Consider the imaginary time Greens function of a fermion field $\Psi(x,τ)$ at zero temperature
$$ G^τ = -\langle \theta(τ)\Psi(x,τ)\Psi^\dagger(0,0) - \theta(-τ)\Psi^\dagger(0,0)\Psi(x,τ) \rangle $$
...
7
votes
0answers
306 views
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; ...
2
votes
1answer
113 views
Good resources for learning/reviewing complex time propagator formalism
I studied this at the beginning of my graduate degree but have to review it for my graduate exam. If it's not clear I'm talking about the $\beta = \frac{it}{\hbar} $ turning the integral of your ...
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votes
4answers
168 views
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 ...
