# Questions tagged [analyticity]

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729 views

### Complex Variable Book Suggestion

What book should I choose to learn complex analysis as a physics Undergrad. I only want to use one book which will contain everything I need.
153 views

### Analytical continuation of 2,3,4-point integrals

I was reading a paper that gives a nice collection of all scalar integrals that crop up in QCD loop calculations. Such integrals are computed in some kinematic region and then the authors say the ...
169 views

### Contour Integration in Deriving Coulomb's Law from Classical Field Theory

This is much more on the mathematical side on the derivation, so I may be barking up the wrong Stack Exchange for this question; however, I have a curiosity about a contour integration performed in ...
361 views

### Why does a shuttlecock flip head down even when dropped head up? [duplicate]

If a shuttlecock is dropped(not giving it any angular momentum wrt it's COM) head up(i.e. the heavier part up) without tilting it, it always falls head down(i.e. the heavier part down). This fact it's ...
213 views

### Sommerfeld expansion for temperature dependent spectral function

Consider the integral \begin{align} I(\beta)=\int_{-\infty}^{\infty}\frac{\text{d}\epsilon}{\pi}\frac{\rho(\epsilon,\beta)}{1+e^{\beta \epsilon}} \end{align} where $\rho(\epsilon,\beta)$ is a generic ...
2k views

### Can scalar quantities have a direction?

Current is a scalar yet it has direction. But ideally, only vectors should possess a sense of direction. Does this mean that even scalars can possess a sense of direction? If yes, can someone give me ...
249 views

### Where is the method of Contour integration used in physics? [closed]

Complex numbers have a wide variety of application in physics and so must be contour integration but where do we exactly apply the principles of contour integration, residues and poles in the field of ...
918 views

### 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 ...
55 views

### X-ray Photoelectron Spectroscopy

Is XPS already an old method? not a lot of new research is produced recently about it. Besides, you can carry out the same analysis by several cheaper methods. Do you think the chemical analysis by ...
90 views

### How do we prove analyticity of Schwinger functions?

Starting from Wightman axioms, we can define the Schwinger functions as the Wick-rotated Wightman functions (as for instance is explained in the book by R. Haag, Local Quantum Physics). The Schwinger ...
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### $\mathrm{i}\epsilon$ prescription makes a function analytical?

I've seen this everywhere where they say "Analytic continuation is obtained by the usual $\mathrm{i}\epsilon$ prescription..." but how is that? How do you analytically continue (say) $\ln x$ with ...
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 ...
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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 ...
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 ...
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 ...
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 ...
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, ...
3k views

### What do the poles of a Green function mean, physically?

Is there a physical interpretation of the existence of poles for a Green function? In particular how can we interpret the fact that a pole is purely real or purely imaginary? It's a general question ...
2k 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 $$G^τ = -\langle \theta(τ)\Psi(x,τ)\Psi^\dagger(0,0) - \theta(-τ)\Psi^\dagger(0,0)\Psi(x,τ) \rangle$$ ...
735 views

### 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 ...
3k views

### 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 ...
491 views

### vector cross products

Lets say you have a free particle in a rotating frame of reference with constant angular velocity $\mathbf{\omega}$. By free, I mean there are no real forces on it. Lets call the moving system "primed"...
758 views

### 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 ...