# Tagged Questions

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### Is the free energy density analytic in temperature at the Kosterlitz-Thouless phase transition?

I know that the KT transition is infinite-order so the free energy density is a smooth (i.e. infinitely differentiable) function of temperature, but is the function actually analytic at the critical ...
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### A problem in an integration related to Wick rotation

In quantum field theory, we often calculate some integrations using Wick rotation. In the following, I will carefully deal with an integration involving Wick rotation. In the end, I have found that I ...
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### How can dimensional regularization “analytically continue” from a discrete set?

The procedure of dimensional regularization for UV-divergent integrals is generally described as first evaluating the integral in dimensions low enough for it to converge, then "analytically ...
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### Non-equivalence between $\omega \to \omega \pm i\varepsilon$ and Cauchy principle value

I am looking to gain a more rigorous and deeper understanding as to how an $i\varepsilon$ prescription actually changes the end result of a divergent integral, specifically in regards to Green's ...
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### Why does analytic continuation as a regularization work at all?

The question is about why analytical continuation as a regularization scheme works at all, and whether there are some physical justifications. However, as this is a relatively general question, I ...
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### Is there an analytical solution for fluid flow in a square duct?

I couldn't find one but assumed it must exist. Tried to find it on the back of an envelope, but got to an ugly differential equation I can't solve. I'm assuming a square duct of infinite length, ...
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### 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 $$G^τ = -\langle \theta(τ)\Psi(x,τ)\Psi^\dagger(0,0) - \theta(-τ)\Psi^\dagger(0,0)\Psi(x,τ) \rangle$$ ...
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### How to parametrize off-shellness?

The energy of a massive on-shell particle of mass $m$ and three-momentum $\vec{p}$ satisfies $$E_\vec{p} = \sqrt{\vec{p}^2+m^2}.$$ What would be the analogous expression for an off-shell particle? ...
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### Are there relativistic theories with spacetime modelled on $\mathbb C^4$ rather than real Minkowski space $\mathbb R^4$?

Does anybody know of references to theories where relativity & spacetime is modelled on a (complex/Kähler) manifold which is locally diffeomorphic to $\mathbb C^4$ rather than $\mathbb R^4$, hence ...
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### A confusion from Weinberg's QFT text (a vanishing term in Lippmann-Schwinger equation)

I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free ...
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### Lippmann-Schwinger Equation with Outgoing Solutions

I'm reading about Green's functions and how the Lippmann-Schwinger equation eventually leads to the textbook expression for the form of wavefunctions in the far radiation zone after scattering by a ...
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### Inverted Harmonic oscillator

what are the energies of the inverted Harmonic oscillator? $$H=p^{2}-\omega^{2}x^{2}$$ since the eigenfunctions of this operator do not belong to any $L^{2}(R)$ space I believe that the spectrum ...
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### Decoupling of Holomorphic and Anti-holomorphic parts in 2D CFT

This maybe a very naive question. I have just started studying CFT, and I am confused by why we have two separate parts of everything in CFT (operator algebras and hilbert space), the holomorphic ...
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### Two similar questions related to analytic continuation of a complex variable and its conjugate

See the scan attached below. Brown, in his QFT book, argues a certain way to do an integral. I understand that 1.8.13 or equivalently 1.8.14 can be performed once analytic continuation is done. I also ...
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### Are Born-Oppenheimer energies analytic functions of nuclear positions?

I am looking for references to bibliography that explores the smoothness and analyticity of eigenvalues and eigenfunctions (and matrix elements in general) of a hamiltonian that depends on some ...