# Questions tagged [analyticity]

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### Why does Taylor’s series “work”?

I am an undergraduate Physics student completing my first year shortly. The following question is based on the physical systems I’ve encountered so far. (We mostly did Newtonian mechanics.) In all of ...
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### Binary Black Hole Solution of General Relativity?

This is rather a technical question for experts in General Relativity. An accessible link would be an accepable answer, although any additional discussion is welcome. GR has well known solutions ...
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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 the step of analytic continuation unavoidable or can you model around it?

One sometimes considers the analytic continuation of certain quantities in physics and take them seriously. More so than the direct or actual values, actually. For example if you use the procedure ...
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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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### What is the intuition behind Kramers-Kronig relations?

I have heard that Kramers-Kronig relations constrains the real and imaginary parts of complex permittivity $\varepsilon= \varepsilon^{'} + j\varepsilon^{''}$. What is the intuition behind this ...
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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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### Where is the Feynman Green's function in quantum mechanics?

In quantum field theory, the Feynman/time ordered Green's function takes the form $$D_F(p) \sim \frac{1}{p^2 - m^2 + i \epsilon}$$ and the $i \epsilon$ reflects the fact that the Green's function is ...
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### What is the significance of the branch cut in renormalization group logarithms?

What is the physical significance of the branch cut in renormalization group logarithms? (Is this just an avatar of the optical theorem, or is there something to be understood about these logarithms ...
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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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### 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 ...
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### Is holomorphicity the real reason for non-renormalization in supersymmetry?

Seiberg traced the nonrenormalization of supersymmetric theories to holomorphicity of the superpotential in chiral superspace. However, this overlooks the fact that with a different number of ...
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### Strange use of complex analysis in Weinberg QFT 1?

In the beginning of chapter 3 on scattering theory in Weinberg's QFT book there is a use of the Cauchy residual theorem that I just cannot get. First some notation, we are looking at states that are ...
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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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### Self-energy that does not obey sum rule

Analytically, I calculated a self-energy $\Sigma(\omega)$, for which I verified that 1) $\text{Im}\big[\Sigma(\omega)\big] \leq 0$ for all $\omega$ and specifically $\text{Im}\big[\Sigma(0)\big] = 0$,...
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### Can we do a Wick rotation by an angle not being $\pi/2$?

If a state obeys an evolution equation, we can replace $t$ by $-t$. we get another equation and it is interesting to study its solutions. If we replace $t$ by $it$ (wick rotation) we get again ...
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### Free energy functions are analytic or non-analytic in phase transitions?

I already saw this Phys.SE post and it seems perfectly reasonable that the free energy describing a system must be a non-analytic function in order to display a phase transition. An analytic ...
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### Renormalization condition: why must be the residue of the propagator be 1

In on-shell (OS) scheme, one of the renormalization conditions is that the propagator, say, a scalar theory $$\frac{1}{p^2+m^2-\Sigma(p^2)-i\epsilon}$$ must have a unit residue at the pole of ...
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### An integral in Peskin's Quantum Field Theory P. 27

In Peskin's QFT P. 27, there is an integral $$-\frac{i}{2 (2 \pi )^2 r}\int_{-\infty}^{\infty} \mathrm{d}p\frac{p\ e^{ipr}}{\sqrt{p^2+m^2}}.\tag{2.51a}$$ He said that in order to push the contour up ...
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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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### Propagator of a real scalar field does not give an unambiguous result

The propagator of a real scalar field is basically a Green function. Its evaluation requires specifying the contour which seems arbitrary. The integral depends on the choice of the contour. For four ...