# 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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### When does the Post-Newtonian expansion break down?

In the book Gravitational waves Vol.1: theory and experiment by M.Maggiore, in chapter 5, page 236, the author discusses the Post-Newtonian (PN) expansion and says that it is valid for small speed and ...
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### Jeans Instability in an Expanding Universe, Understanding the perturbation

I am trying to derive the equation for a case, where we have a dust(zero-pressure) in an expanding universe. There are 4 equations but I think exercising on one of them would be helpful for me. So ...
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### Feyman diagrams on the basis of counterterms of the $\phi^4$ theory

I would like to understand how the Feyman rules for counterterms are derived. For this reason I start with following, certainly a bit naive approach inspired by Peskin & Schroeder. Once the ...
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### When is a parameter considered small for perturbation and how does physical units affect that?

In perturbation theory procedures (not specific to any particular topic) we tend to have (or delibrately insert) some small variable $\epsilon$ in an equation that is otherwise difficult to solve if ...
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### Are the matrix elements of $S$-matrix Lorentz invariant?

In quantum field theory, the $S$-matrix is defined as a time-ordered exponential $$S=T\Big[\exp\Big(-i\int d^4x \mathcal{H}_{\rm int}\Big)\Big].$$ Since $\mathcal{H}_{\rm int}$ is a combination of ...
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### Error estimation for field theories

I am looking for resources on error estimation for field theories, both the error due to perturbation theory and measurement error. In other words, consider a field theory of a field $\phi$, with some ...
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### Degenerate perturbation theory in classical mechanics

I would like to know if there is a way to properly do time-independent degenerate perturbation theory in classical mechanics. Any answer or pointer to a good source would be appreciated. The issue of ...
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### Can you explain DFT and TDDFT functioning (math aside)?

I have been recently reading a lot on the quantum mechanical theory regarding Density Functional Theory, DFT and Time-Dependent Density Functional Theory, TDDFT (Oscillatory and Rotatory Strengths in ...
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### A question about Dyson's argument of divergence of perturbative QFT

Related question Doubt in Dyson's argument about the divergent nature of the perturbative expansion in QED My question is, suppose $e^2<0$ and the aggregations of the same type of charge, ...
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### If the running coupling constant $\alpha(\mu)$ of QED becomes of order one at high $\mu$, why not changing $\mu$?

In the (modified) MS renormalization scheme, after dimensional regularization, we introduce some parameter $\mu$ with power of mass to keep the dimensionality of integrals under control. The ...
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### Perturbing the Harmonic oscillator [closed]

Assume that a quantum harmonic oscillator is described by the Hamiltonian, \begin{equation} H=H_0+\lambda q^2 \end{equation} where, \begin{equation} H_0=\frac{p^2}{2m}+\frac{1}{2}m\omega^2q^2 \end{...
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### How do physicists use the Feynman path integral practically?

I somewhat understand how the path integral works in simple examples, I just don't get how someone can add up an infinite amount of paths. How is that even calculated? If it's got something to do ...
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### Power counting and divergences

Often, in many books such as Peskin and Schroeder, a Feynman diagram or the effective potential is expanded as a function of the external momenta or the classical fields respectively. Consider the ...
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### When can $H = H_0 + \lambda V$ be perturbed in a weak interaction?

Consider a finite-dimensional free Hamiltonian $H_0$, interaction $V$ and dimensionless coupling $\lambda \ll 1$ so that $$H = H_0 + \lambda V \ .$$ My question is, when is one allowed to perturb ...
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### Time Dependent Perturbation theory normalization and the driven Harmonic Oscillator

I was working out a problem from Sakurai's quantum mechanics (Problem 5.22) and it caused me to questions something I thought I knew. The problem effectively says to consider a driven harmonic ...
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### Feynman rules and the hydrogen atom

In his Quantum theory of fields, Vol. 1, Weinberg claims that the old-fashioned perturbation theory allows studying an appearance of singularities in matrix elements by intermediate states. As an ...
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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 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 ...