# Questions tagged [asymptotics]

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### Is QED asymptotically free in lower dimensions?

It is well-known that QED (=quantum electrodynamics) is NOT asymptotically free in spacetime dimension $4$. However, I wonder if it becomes asymptotically free in lower dimensions, such as $2+1$ ...
79 views

### Leading order of integrals in Field Theory

I am studying Statistical Field Theory from the notes of D. Tong (http://www.damtp.cam.ac.uk/user/tong/sft.html). I have trouble to understand how to estimate the leading order of diverging integrals ...
95 views

### How does asymptotic analysis work with quantum mechanics?

I am trying to wrap my head around asymptotic analysis when it is applied to quantum mechanics. The best source I have found so far is from MIT (https://ocw.mit.edu/courses/8-04-quantum-physics-i-...
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### Definition of Asymptotically Flat at Null, Spacelike, and Timelike Infinities

Most books I've looked into discuss asymptotic flatness in general relativity for the null and spacelike case (e.g. Wald), or for the null and timelike case (e.g. arXiv: 1706.09666 [math-ph]), but I ...
63 views

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### Are all asymptotic symmetries and their meaning known?

Beyond the Standard Model and the General relativity invariant groups, recently we have met (again) the BSM groups of asymptotic symmetries given by the Bondi-Metzner-Sachs (BMS) or the extended BSM ...
190 views

### What are the Maxwell equations of motion in retarded Bondi coordinates?

I'm reading a paper about asymptotic symmetries at null infinity in electrodynamics. There, they had the following calculation: The Maxwell equations $\nabla^{\nu} F_{\mu\nu} = J_{\nu}$ written in ...
209 views

### Can energy levels rise faster than $n^2$?

For a 1D particle in a box, energy levels are exactly proportional to $n^2$. For the harmonic oscillator, $E_n\sim n$. And for a particle in an $|x|^\alpha$ potential, the energies are $\sim n^\beta$ ...
137 views

### Why is it that in gauge theories the assumption "all fields decay sufficiently rapidly at infinity" not justified anymore?

I read that in gauge theories the assumption that "all fields decay sufficiently rapidly at infinity" is not justified anymore and therefore, one needs to consider boundary terms that ...
62 views

### How can can we show that a metric is asymptotically AdS?

Given any metric, for example $$ds^2=d\tau^2+L^2\cosh(H\tau)d\vec{x}^2$$ how can we show that this metric is asymptotically Euclidean AdS? Specicifally, when $\tau\rightarrow\pm\infty$ is it ...
179 views

### Fokker-Planck: uniqueness and convergence to stationary distribution

Consider the Langevin equation ($N$-dimensional) with nonlinear drift term, but expressible as a gradient of a function $U(\vec{x})$. Namely, consider the stochastic process described by the set of ...
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### Question about field configurations on the boundary of $\mathcal{I}^+$

I am reading Strominger's lecture notes "The infrared structure of gravity and gauge theory" (https://arxiv.org/abs/1703.05448). In chapter two, while trying to derive an expression about ...
210 views

### In and out states of scattering in Asymptotically flat spacetimes

I am reading a paper called "New symmetries of massless QED", written by Temple He, Prahar Mitra, Achilleas P. Porfyriadis and Andrew Strominger (https://arxiv.org/abs/1407.3789). At some ...
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### Was asymptotic expansion also a form of symmetry?

Consider the infinitesimal expansion, which was used to describe the behavior of of the expression when taking the parameter to be small. The infinitesimal expansion was usually used to describe the ...
261 views

### A calculation of microstates

Pathria, Statistical mechanics pg 11,4ed In order to find the number of microstates $\Omega(N,V,E$) author writes " In other words, we have to determine the total number of (independent) ways of ...
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