# Questions tagged [perturbation-theory]

Perturbation theory refers to methods for understanding physical systems by treating them as small modifications to exactly solvable systems.

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### Schrieffer-Wolff Transformation for conventional superconductors

I was trying to follow the discussion in Radi A. Jishi's book (Feynman Diagrams in Condensed Matter Physics), Chapter 12 on superconductors. They basically have a Hamiltonian that comprises of a ...
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### Rigorous proof of Bertrand's Theorem for orbits under central force

I have read through several proofs of Bertrand's Theorem, including the one on Wikipedia. A typical proof can be found here (Santa Cruz Institute for Particle Physics). Almost all proofs using ...
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### Diffeomorphism for Equation of motion in Brans Dicke theory

I am trying to see the gauge invariance, (diffeomorphism) for equations of motion in Brans-Dicke theory. Frist the equation of motion is given as follows, [I just copied from Wikipedia] \begin{...
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### What is the difference between Lamb shift and the Darwin term?

I am currently learning for an exam and I wonder what the difference between the Lamb shift and the Darwin term is. What I know is that the Darwin term affects only the s-states of the hydrogen atom ...
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### What does it mean to study transition probability?

I'm starting to study time-dependent perturbation theory. The book applies time-dependent perturbation on the hamiltonian and it says that for this reason quantum transition are allowed. Then it ...
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### Borel Resummation on a finite asymptotic series

I am reading http://users.physik.fu-berlin.de/~kleinert/kleiner_reb8/psfiles/16.pdf I am a little confused on the use of the Borel Transform in perturbative series. I know that Green's Functions in ...
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### couplings between mesons and baryons (singlet and octet)

What is the basic meaning and good reference for the deep and simple meaning(in simple language) of couplings between mesons and baryons, e.g., g1 and g8 couplings (singlet and octet) from where these ...
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### What are “the background equations” in cosmology?

We're currently working on perturbations within cosmology. There is something I have not heard before which has cropped up, that is: a reference to the term "the background equations". Are these just ...
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### What is Wick's theorem and what this is use for? [closed]

I am reading Wick's theorem but although I look for it to clearly understand in some textbooks and youtube videos but still it is unclear to me. I cannot get my head over what is normal ordering ...
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### Inversion of a metric

I am currently reading a paper by Bredberg $et.al$ arXiv:1101.2451 titled "From Navier-Stokes to Einstein". In this paper, the authors have considered a metric of the form \begin{eqnarray}ds^2_{p+2} = ...
143 views

### Dealing with degeneracy in Paschen-Back Effect

Suppose there's a strong external magnetic field applied on a Hydrogen-like atom. The Hamiltonian due to spin-orbit coupling will have much less effect compared to the other Hamiltonians. I would ...
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### Perturbed Ricci scalar in Modified Gravity

When getting the perturbed Ricci scalar in a Modified Gravity theory of the form $\mathcal{L}_{gr}=F\left(\phi,R\right)R$, $\phi$ being a scalar field, it is easy to arrive at an expression of it in ...
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### Perturbation theory with infinite potential

I'm trying to solve an excercise that involves first order perturbation theory and an infinite potential. To ease the problem, I tried to consider an easier one dimensional model. Consider an infinite ...
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### Relation Asymptotic Series and perturbative effects

Perturbative expansions of a function $f(x)$ around say $x=0$ cannot determine contributions from a function such as $e^{-1/x}$ since its Taylor series vanishes to all orders. This kind of ...
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### Relativistic correction to Hydrogen atom - Perturbation theory

Given the relativistic correction $$H_1' = - \frac{p^4}{8m^3 c^2}$$ to the Hamiltonian (i.e. a perturbation), what does it mean when $[H_1', \mathbf{L}] = 0$? The book I'm reading says this implies ...
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### Cosmology - Demonstration for equation of the evolution of the density contrast

In a context of cosmology, I need help about a differential equation that I can't get to demonstrate: The growth of density fluctuations obeys a second order differential equation. At early enough ...
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### Mechanism behind spin orbit interaction

The spin orbit coupling can be explained through two different frames one is the electron frame and the other, the lab frame. In the electron frame magnetic field produced by proton current current ...
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### What happened to the factor of $\pi$ in this question?

$\\$ I was going through the answer to this problem, when I noticed that a factor of $\pi$ in the denominator disappeared and a factor of 4 appeared in the numerator when the author started ...
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### Optical theorem in $\phi^4$: which poles contribute to discontinuity in Feynman amplitude?

Section 7.3 ("The Optical Theorem") in Peskin and Schroeder's QFT text contains a leading order verification of the optical theorem in $\phi^4$ theory by calculating the (discontinuity across the ...
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### Why do we need the coupling small when doing perturbative QFT calculation?

I don't really understand why, when we calculate say the 2-point Greens function in a scalar QFT with interaction $\lambda \phi^4$, we need the coupling constant $\lambda$ to be small? Everywhere I ...