Questions tagged [perturbation-theory]

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

Filter by
Sorted by
Tagged with
2
votes
0answers
73 views

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 ...
2
votes
1answer
52 views

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 ...
1
vote
0answers
20 views

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 ...
0
votes
1answer
52 views

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 ...
1
vote
0answers
38 views

Confusion about calculating first order correction to energy eigenstate / state vector

I am trying to determine the first order correction to the ground state for a particle in an infinite square well with a given perturbation, $$V'(x) = \frac{2\pi^2 h^2}{mL^3} (\epsilon x- \frac{\...
0
votes
0answers
7 views

Momentum matrix elements for two-photon absorption in semiconductors

I am trying to follow the paper "Two-photon absorption with exciton effect for degenerate valence bands" (to be found here: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.9.3502). It gives the ...
2
votes
0answers
38 views

Keldysh Field Theory: Self Energy Structure in RAK basis

Consider the Keldysh formulation of electrons interacting with each other through the Coulomb potential. Suppose that we've switched to the RAK (Retarded-Advanced-Keldysh) basis of Larkin & ...
1
vote
0answers
21 views

Interactions other than yukawa interaction which results in pair annihilation

Can boson annihilates to an electron positron pair can happen in all type of interactions which contains some number of dirac fields coupled with some number of bosonic fields? I asked this question ...
1
vote
0answers
36 views

Delta function in Fermi's Golden rule [duplicate]

I am currently trying to understand the Fermi's golden rule. We consider a system with Hamiltonian: $$\hat H = \hat H_0 + \hat Ue^{i \omega t},$$ where the expectation value of $\hat U$ i much ...
1
vote
1answer
64 views

Is there any book that treat time-dependent perturbation theory with rigorous mathematics?

I am searching for rigorous mathematics books or notes for time dependent perturbation theory. For introductory quantum mechanics there is the excellent book spectral theory and quantum mechanics ...
1
vote
1answer
77 views

Book suggestion about Neutrino effect on Cosmic Structure

I am trying to find some nice explanatory books about neutrino effects on the cosmic structure. I did not take GR so I prefer sources that contain not much GR. I prefer lecture note series or books ...
1
vote
0answers
38 views

Semiconductor equations

I am starting off on a solar cells project. I am a mathematics undergraduate and the main focus of the project is exploration of different analytical solutions to the basic system of equations (...
1
vote
1answer
36 views

How to calculate the second order pertubation in an electron gas?

This problem is from the book Quantum theory of many particles systems by Fetter & Walecka (1971), exercise 1.4. Problem discription: The Hamiltonian could be divided into $$H_0=\sum_\limits{\...
3
votes
2answers
134 views

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 ...
2
votes
0answers
24 views

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 ...
0
votes
0answers
50 views

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 ...
2
votes
2answers
97 views

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 ...
1
vote
3answers
92 views

What is the nature of perturbation theory in QFT?

In the perturbation theory approach to QFT, the total Hamiltonian $H$ is separated into a free part $H_0$ which we can solve exactly and another $H_{\rm int}$ which we cannot such that $$H=H_0+H_{\rm ...
0
votes
0answers
33 views

Perturbation theory classical and quantum physics

I have calculated the correction in frequency for harmonic oscillator potential with the perturbation $x^4$ both classical mechanically (Lindstedt-Poincaré technique)and quantum mechanically. And I ...
0
votes
0answers
29 views

Time-independent perturbation theory

Considering the analytic expansion $$\left|E_{\lambda}\right> = \left| \alpha \right> + \lambda \left| \beta \right> + O(\lambda^2).$$ Why can we write $\left| \beta \right> = \sum b_n \...
1
vote
0answers
31 views

How to derive the perturbativity condition of a simple Kaluza-Klein theory?

I thought that the simple $\lambda\phi^4$ theory in 4D is always perturbative if $\lambda<1$. Below equation 107.1, PDG review of extra dimensions says that the 5D Kaluza-Klein theory $$S_5=-\int ...
1
vote
0answers
45 views

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, ...
0
votes
2answers
66 views

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 ...
1
vote
2answers
70 views

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{...
3
votes
0answers
106 views

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 ...
1
vote
1answer
74 views

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 ...
0
votes
1answer
35 views

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 ...
0
votes
0answers
20 views

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 ...
0
votes
0answers
34 views

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 ...
2
votes
0answers
71 views

What is a reason for the energy to not conserve in QM perturbation theory?

Consider the transition rate of the evolution of the state $|i\rangle$ to a state $|f\rangle$ - the Fermi golden rule: $$ d \omega_{if} = 2\pi |\mathcal{M}_{fi}|^{2} \delta(E_{f} - E_{i})d\nu, \quad \...
1
vote
0answers
52 views

Using second order perturbation to calculate electron self-energy caused by electron-phonon interaction

Assume the electron-phonon interaction is given by $$ H_{ep} = \sum_{k q} D(q) c_{k+q}^\dagger c_k (a_q + a_{-q}^\dagger). $$ In the theory of superconductivity, the electron-electron effective ...
0
votes
0answers
38 views

Fermi’s golden rule integral over energy states, time constraints

In perturbation theory, we can, to first-order, arrive at an expression for transition rates that looks like $$ \Gamma = \frac{2}{\hbar} |M_{if}|^2 \frac{\sin{\frac{E_f-E_i}{\hbar} t}}{E_f-E_i}. $$ ...
6
votes
2answers
601 views

What's the difference between perturbative QCD, non-perturbative QCD, and gauge theory QCD?

I'm trying to get the ideal of QCD, and it turns out that there seems to be several versions, and some of which does not appear to agree with each other at a glance. What's the difference, and how ...
0
votes
2answers
76 views

Understanding the meaning of “Orders” in Perturbation Theory in Quantum Mechanics

While learning time-independent perturbation theory, there was something that I couldn't understand, and it has to do something with order of $\lambda\\$ For example, when deriving the equation for ...
2
votes
0answers
29 views

Rigorous adiabatic elimination for $N$-state quantum system under harmonic perturbation

I am interested in a rigorous derivation of the coherent evolution of a quantum system with $N$ states under the application of a harmonic perturbation. I have read several articles about the use of ...
1
vote
0answers
33 views

Calculating $\nabla_\mu T^{\mu\nu}$ in linear cosmological perturbation theory

I am trying to calculate $\nabla_\mu T^{\mu\nu}$ for perfect fluid in the context of the linear cosmological perturbation theory. I'm working in the Newtonian gauge. I have successfully calculated $\...
0
votes
1answer
96 views

Transition probability in the case of “strong” perturbation

We know that Fermi's Golden rule is true only for weak and short perturbation, when the transition probability $P_{fi}\ll 1$. But what if perturbation is relatively strong, so we can't use this ...
0
votes
1answer
34 views

How does a multiple timescale analysis work?

I often see papers which analytically solve a set of ODEs taking into account the different timescales over which each of the variables change. For example, one might have a set of ODEs $$\frac{dA}{...
3
votes
0answers
56 views

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 ...
0
votes
1answer
91 views

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 ...
0
votes
0answers
15 views

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{...
0
votes
0answers
22 views

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 ...
0
votes
0answers
39 views

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 ...
0
votes
0answers
15 views

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 ...
2
votes
1answer
66 views

Perturbation Theory - Exact Solutions and Good Quantum States

I'm having a problem with the following question: Problem: Consider the unperturbed, degenerate Hamiltonian $H_0=\bigg(\begin{matrix} E &0\\ 0& E\end{matrix}\bigg)$. Add the perturbation $...
4
votes
2answers
367 views

Struggling to understand degenerate perturbation theory

As far as I gather, before a perturbation is applied, the eigenspace associated with the degenerate energy is multidimensional but after applying the perturbation this space 'splits' into different ...
0
votes
0answers
21 views

First Order vs. Second Perturbative Transition Probabilities with Unruh deWitt Detectors

I have been working with perturbative expressions for the transition probability/rate of an Unruh deWitt detector. Many papers such as this one - https://arxiv.org/pdf/gr-qc/0606067.pdf - seem ...
0
votes
1answer
38 views

What's the most general approach to Zeeman effect?

I have a question regarding the Zeeman effect and perturbation theory in the hydrogen atom. We have hamiltonian of the hydrogen atom is given by $H_0$, that of spin-orbit coupling given by $H_{\text{...
0
votes
0answers
56 views

Problem in odd-even decomposition of a generic metric

The metric of the unit two-sphere is given by $ \Omega_{\mu \nu} = \begin{equation} \begin{pmatrix} 1 & 0 \\ 0 & \sin^2 \theta \end{pmatrix}. \end{...
0
votes
1answer
83 views

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 ...

1 2 3 4 5 14