# Questions tagged [asymptotics]

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### Asymptotic states and physical states in QFT scattering theory

Context In the scattering theory of QFT, one may impose the asymptotic conditions on the field: \begin{align} \lim_{t\to\pm\infty} \langle \alpha | \hat{\phi}(t,\mathbf{x}) | \beta \rangle = \sqrt{Z} \...
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### How to state that a function has a certain andament in a limit? [migrated]

Assuming we have a function $f(r)$ that has the following limit $$\lim_{r\to0} f(r) = \frac{5}{3 r^2} \,.$$ What is the correct symbol to express that the denominator goes like $r^2$? Is the ...
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### Long-range approximations of the Uehling interaction

A common approximation to the U(\vec{r})=-m\frac{\alpha(Z\alpha)}{\pi} \int_1^\infty\mathrm{d}u\frac{\sqrt{u^2-1}\left(2u^2+1\right)}{3u^4}\frac{\exp(-2mur)}{mr} \tag{$\star$} \end{...
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### Calculating LSZ reduction for higher order in fields terms

Consider a theory with only a single massless scalar field $\phi(x)$ and a current $J^\mu(x)$ which can be polynomially expanded as fields and their derivatives and spacetime \begin{align} J^\mu(x) = ...
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### What goes wrong with strongly coupled theories?

Let $\lambda$ be the coupling constant of a quantum field theory. It is said that Perturbation theory is only valid when the theory is weakly coupled ($\lambda \ll 1$). In most cases, the series of ...
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### Asymptotic form of solution to biased random walk

(Cross post from math.stackexchange) Consider a continuous time biased random walk on a 1D lattice. The random walker walks with rate $k_\mathrm{R}$ to the right and with rate $k_\mathrm{L}$ to the ...
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### Riemann-Lebesgue lemma in Faddeev-Kulish approach

I am learning about the established formalism used in the literature of IR divergences and dressed states, and I invariably come across an argument of the following form when evaluating a (photon) ...
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### Why do we use perturbative series if they don't converge?

My course instructor mentioned that the Perturbative Series are not convergent but diverge as we consider more and more terms in the expansion. He then briefly mentioned that the Perturbative Series ...
• 317
1 vote
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### Energy gap of mean field model for transverse ising chain

Polynomials of spin operators with real coefficients appear not infrequently in Hamiltonians and in mean field theory, and there are often tricks to find their eigenvalues. For example, the polynomial ...
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