# Questions tagged [asymptotics]

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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 ...
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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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### Thought experiment on boundary condition of galaxies

A thought experiment: Let's assume that there is only one single galaxy in the whole universe. How would it look like regarding the curvature of spacetime? Would the spacetime be flat in the infinity ...
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### Free massive propagator as an OPE?

Consider a free massive propagator $$G(p)\equiv\frac{1}{p^2+m^2}$$ There is a 'naive' expansion in terms of the mass $$G(p)\sim\sum^\infty_{n=0} (-1)^n \frac{m^{2n}}{p^{2(n+1)}}$$ This expansion might ...
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### How and why the state of free particle in quantum physics is represented by plane wave packet? [closed]

In Quantum Mechanics (Cohen Tannoudji) Topic: "Asymptotic Form Of Stationary Scattering States" It is written that for large negative values of $t$, the incident particle is free and it's ...
• 67
1 vote
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### Analysis of the eigenvalues of the particle in a finite square well

The eigenstates of the particle in a 1D finite square well Hamiltonian: \begin{align} H = \frac{\hat{p}^2}{2m} + V(x) \end{align} \begin{align} V(x) = \begin{cases} -V_0 & \...
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### Divergent Energies and Analytical Continuation - Two questions on the inverted harmonic oscillator and the inverted double well

I have two questions on the general topic of energy potentials that diverge at infinity. First of all, the inverted harmonic oscillator. I found this post on Physics SE, Inverted Harmonic oscillator. ...
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### Confusions on expectation value for $\hbar$ going to zero

In Matthew D. Schwartz's QFT book, Chapter 28, the author claims when $\hbar \rightarrow 0$, the following equality (eq 28.4) holds: So how can I see the second "$=$" holds? It seems the ...
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### Past boundary of $\mathcal{I}^+$ and future boundary of the hyperboloid resolving $i^0$

Let us consider Minkowski spacetime. Let $(u,r,x^A)$ be retarded coordinates with $x^A$ coordinates on the sphere. Future null infinity is described here as the $r\to \infty$ limit with $(u,x^A)$ ...
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### Why can I not asymptotically expand a Feynman integral this way?

I would like to asymptotically expand a series of Feynman diagrams in Euclidean space, and as a toy I started with the following integral, for which I know the full solution in $4d$ ($\omega \to 2$): ...
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