# Questions tagged [analyticity]

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While it is quite common to use piecewise constant functions to describe reality, e.g. the optical properties of a layered system, or the Fermi–Dirac statistics at (the impossible to reach exactly) $T=... 1answer 1k views ### Landau & Lifshitz's Approach (contour method) on the WKB connection formulas Background of the question (see pp. 161, section 47 in Landau & Lifshitz's quantum mechanics textbook Vol3, 2nd Ed. Pergamon Press). We a following potential well $$U(x)\leq E \quad\text{for} \... 7answers 1k views ### 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 ... 2answers 5k views ### Gaussian integral with imaginary coefficients and Wick rotation Although this question is going to seem completely trivial to anyone with any exposure to path integrals, I'm looking to answer this precisely and haven't been able to find any materials after looking ... 5answers 556 views ### Does the mass point move? There is a question regarding basic physical understanding. Assume you have a mass point (or just a ball if you like) that is constrained on a line. You know that at t=0 its position is 0, i.e., ... 2answers 5k views ### 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, ... 2answers 713 views ### 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 ... 1answer 1k views ### Concrete example of the application of complex analysis in electrostatics [closed] I've heard complex analysis can be useful in solving electrostatics problems, but despite doing some research I was unable to find any concrete examples. Would anyone be able to provide a simple ... 2answers 271 views ### Using Wick Rotation to calculate Generating Function in Minkowski Space The question arises when I'm reading over the section "3.3.1 Minkowski Space" in page 16-17 in the following link: https://www-thphys.physics.ox.ac.uk/people/JohnCardy/qft/qftcomplete.pdf It is ... 2answers 2k views ### 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 ... 5answers 664 views ### Why is analyticity a good mathematical assumption in general relativity? In general relativity, real-variable analytic continuation is commonly used to understand spacetimes. For example, we use it to extend the Schwarzschild spacetime to the Kruskal spacetime, and also ... 2answers 1k views ### 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}$$and the i \epsilon reflects the fact that the Green's function is ... 1answer 716 views ### From Minkowski to Euclidean Time in Path Integrals I'm trying to prove the following equality:$$ <x_{f},\, it_{f}|x_{i},\, it_{i}>=\mathcal{N}\int_{\left\{ x\in\mathbb{R}^{\mathbb{R}}:\, x\left(t_{f}\right)=x_{f}\wedge x\left(t_{i}\right)=x_{i}\... 1answer 972 views ### 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 ... 1answer 283 views ### 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 ... 2answers 1k views ### 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 ... 2answers 1k views ### 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 ... 3answers 2k views ### 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 ... 2answers 196 views ### Radial ordered commutation relation In the book Conformal Field Theory of Francesco, Mathieu and Sénéchal, in Sec. 6.1.2, the authors state that the integral $$\oint_w \mathrm{d}z~ a(z)b(w) ~=~ \oint_{C_1} \mathrm{d}z~ a(z)b(w) - \... 2answers 849 views ### Lippmann-Schwinger Equation with Outgoing Solutions I'm reading about Green's functions and how the Lippmann-Schwinger equation eventually leads to the textbook expression for the form of wavefunctions in the far radiation zone after scattering by a ... 1answer 631 views ### Must the wavefunction be (real) analytic? In order to show the preservation of normalization of the wave function (in one dimension for now), one shows that the time differential is zero, which entails the following step:$$ \frac{d}{dt}\... 0answers 144 views ### What is radial ordering? In my String theory lecture radial ordering was introduced and I don't understand what it is. My first guess was $$R(A(z)B(w)) = A(z)B(w)\Theta(|z|-|w|) + B(w)A(z)\Theta(|w|-|z|).$$ But then we have ... 1answer 57 views ### Is this a holographic principle? The idea of the holographic principle is that all the data about what's inside a volume can be discribed by fields on it's boundary. But... isn't this just obvious calculus? e.g. take a field in ... 1answer 58 views ### Method of pole shifting (feyman's trick) in Scattering theory vs contour deformation trick I am studying Scattering theory but I am stuck at this point on evaluating this integral$G(R)={1\over {4\pi^2 i R }}{\int_0^{\infty} } {q\over{k^2-q^2}}\Biggr(e^{iqR}-e^{-iqR} \Biggl)dq$Where$ ...
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 ...