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
\begin{equation}
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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Asymptotics of 2D Ising model transfer matrix eigenvalues
The NN 2D Ising Model at inverse temperature $\beta$ and external magnetic field $h$ on an $L_1\times L_2$ sized box within $\mathbb{Z}^2$ with periodic boundary conditions $$\sigma_{L_{1}+1,x_{2}} = \...
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How does the asymptotic metric fluctuation in $n \to m$ scattering relates to the soft factor in Weinberg's soft graviton theorem?
I'm reading arXiv: 1411.5745 [hep-th]. In Sec. 5, the authors show how the memory effect and Weinberg's soft graviton theorem are two faces of the same coin. I'm interested in understanding a specific ...
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Introductory references on the gravitational memory effect
I'm currently reading Andrew Strominger's Lectures on the Infrared Structure of Gravity and Gauge Theory. While I love the reference, the discussion on the gravitational memory effect feels a bit ...
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Expression of $\langle 0 | 0 \rangle _{f,h}$ in the Srednicki's quantum field theory book (eq. (6.21), p.47) [duplicate]
I am reading the Srednicki's quantum field theory book and stuck at some statement. In the book p.46, the author worte that :
"Now consider modifying the lagrangian of our theory by including ...
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Gauge symmetries, isometries of spacetime and asymptotic symmetries
I am having a hard time understanding the physical meaning of asymptotic symmetries in General relativity. I think I understand the mathematics, but the meaning eludes me. I'll try to write the things ...
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Do supertranslations act in a physically nontrivial way?
I'm currently reading arXiv: 1703.05448 [hep-th]. In this question, I'm interested in a statement made on page 67 of the pdf (76 of the printed book, if you prefer to check in it). There, the author ...
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Next-to-leading $1/N$ contributions to Feynman diagrams in large $N$
I want to understand $1/N$ contributions to quark bilinear operators $J(x)$ in large $N$, for instance, operators of the form $q\bar{q}$ or $\bar{q}\gamma^\mu q$. As pointed out by E. Witten, in the ...
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Examples of spacetimes that are asymptotically flat at future timelike infinity
There are interesting non-trivial examples of spacetimes which are asymptotically flat at null and spacelike infinities. For example, the Kerr family of black holes satisfies these conditions. However,...
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What are Supertranslations and Superrotations in General relativity, and how does it inform us about a detector at null infinity?
How did I get here?
While drafting my question, I found this very similar question on our site.
Three days ago, I happened upon the concept of supertranslations and superrotations in General ...
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