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
0
votes
0answers
10 views

Parametrising Perturbations with Linear Momentum in GR

In general relativity it is sometimes said that one can parametrise perturbations of a spacetime by characterizing the perturbations with a parameter like the linear momentum. I'm not sure how this ...
2
votes
2answers
55 views

Perturbation Method: What is the acceptable method to terminate expansion

I am using the book Classical Dynamics of Particles and Systems by STEPHEN T. THORNTON, JERRY B. MARION, page: 67 and they use perturbation method to approximate: \begin{equation} T = \frac{kV + g}{...
3
votes
1answer
42 views

Homogeneous solutions in the renormalization-group pertrubation method

I am trying to get a handle on the renormalization-group approach to perturbation theory. I understand the overarching approach, but I'm stumbling on the mechanics of early steps when actually doing ...
0
votes
0answers
27 views

Perturbation theory for a band model

I am considering a set of stationary states $\psi_{kn}$ where $k$ is the wavenumber and $n$ labels the states for a particular value of $k$. I want to see the effect the perturbation of an electric ...
0
votes
1answer
49 views

Change in wavefunction due to adiabatic potential in time dependent perturbation theory

I've been puzzled equation (2.2) of this paper, I've looked into time-dependent perturbation theory and the adiabatic theorem and the closest I could come to deriving this was showing that $$ i \hbar ...
1
vote
0answers
81 views
+50

Linear response theory for a condensed matter system

i'm trying to understand the derivation pictures below for a perturbation in the form of an electric field on the lattice. I understand that in time independent first-order perturbation theory, we ...
-1
votes
0answers
42 views

"Absorbing" UV divergences

What does it mean when someone writes that a finite number of parameters "absorb" the UV divergences of a perturbatively renormalizable theory? Is there a physical interpretation to this?
1
vote
1answer
47 views

Finding the first-order perturbation of the energy of a hydrogen atom due to Spin Orbit coupling

I am given an exercise on perturbation theory involving an electron in a hydrogen atom in the presence of a constant magnetic field $\vec{B} = B_z \hat{z}$. Due to Zeeman effect and Spin-Orbit ...
2
votes
1answer
64 views

What justifies regularization with a high-momentum cutoff?

Before renormalizing a perturbative series, during the regularization step when we insert a high-momentum UV cutoff, what justifies this step given that it's only formal and does not have a physical ...
0
votes
0answers
52 views

Perturbative renormalization as re-parametrization

I've read that the source of UV divergences in perturbative renormalization is due to a bad choice of parametrization. But since we have some freedom over how to reparametrize, and some of them are &...
0
votes
0answers
21 views

Epstein-Glaser renormalization and perturbative renormalization

I am trying to understand the differences between perturbative renormalization and Epstein-Glaser renormalization, which conceives of renormalization as the extension of distributions. What is ...
0
votes
0answers
10 views

Understanding the Quantum Conductivity Tensor in Crystals in Agranovich and Ginzburg

I've been reading Crystal Optics and Spatial Dispersion by Agranovich and Ginzburg and have been confounded by a step in their derivation of the conductivity tensor in crystals. They begin with the ...
0
votes
2answers
65 views

Perturbation theory and size of the perturbation

In quantum field theory, we usually perturb the free field by a little bit. What would be so bad about using a large perturbation to the free field?
0
votes
0answers
38 views

Perturbation theory for triangular barrier

My teacher asked us to use perturbation theory to get the energy of the ground state in such potential: $$ V = \left \{ \begin{aligned} \infty \quad x < 0 \\ Ax \quad x \geq 0 \end{aligned} \right ...
0
votes
1answer
51 views

Relationship between good quantum numbers and degenerate perturbation theory

I'm currently studying time-independent perturbation theory and I ran into a couple of doubts that for the life of me I can't seem to solve. A "good quantum number" is the eigenvalue of an ...
0
votes
0answers
57 views

Asymptotic behaviour of a non-linear differential equation in Gravitation

I have been recently working on modifications to General Relativity, by adding new curvature terms in the Lagrangian density of the theory. In one of these theories (Einsteinian Cubic Gravity), the ...
2
votes
1answer
68 views

Details of using flat metric to raise/lower indices in linearized GR. I'm getting first order discrepancies

This question is about the use of the unperturbed (Minkowski) metric $\eta_{\mu\nu}$ (and its inverse $\eta^{\mu\nu}$) to raise and lower indices in linearized gravity. There are already several ...
7
votes
3answers
887 views

What do the off-diagonal elements of Hamiltonian matrix physically represent?

A briefly question: what's the "physical meaning" of the off-diagonal elements of Hamiltonian matrix? Such as an Hamiltonian Matraix looks like: $$\hat H = \begin{pmatrix} E_{11} & E_{12}...
0
votes
1answer
39 views

A poorly posed time dependent perturbation benzene type ring question

In my first year masters QM class my professor recently mentioned an example that he said he would either give on an assignment or possibly put on our exam. We have all our assignments now and it hasn'...
1
vote
1answer
124 views

Action perturbation vs Equation of motion perturbation

I have a simple question which has been in my mind for some time and I would be thankful if anyone help me to fix it. Consider the following action : \begin{equation} S=\int\!dt\,({\textstyle\frac12}\...
9
votes
1answer
623 views

Why do people care so much about 'linear response theory'?

In the lectures I've heard linear response theory was introduced multiple times, however I can't tell how this is any different from solving an inhomogeneous PDE with a greens function and there's ...
10
votes
1answer
192 views

What is the current status of the convergence of the post-Newtonian approximation?

In the very well written article by C. Will, On the Unreasonable Effectiveness of the post-Newtonian Approximation in Gravitational Physics, he states: The one question that remains open is the ...
5
votes
2answers
338 views

Why does perturbation theory involve a Taylor series rather than a Laurent series?

Perturbation theory in the QM and the QFT is usually explained in terms of a small parameter expansion $\epsilon$ and expanded in a Taylor series. $$O(t)=O_0(t)+\epsilon O_1(t)+\epsilon^2 O_t(t)+...$$ ...
1
vote
1answer
70 views

Wheeler-Regge analysis of $R \neq 0$ metric

I am trying to do a Wheeler-Regge analysis of a Morris-Thorne wormhole, but unfortunately, the Morris-Thorne wormhole is not Ricci-flat i.e. $R \neq 0$ where $R$ is the Ricci scalar, therefore, I am ...
0
votes
0answers
19 views

Iterative block diagonalisation in degenerate perturbation theory

How is iterative block diagonalisation carried out in the matrix form of degenerate perturbation theory to lift degeneracy present in the zeroth-order or unperturbed Hamiltonian ($H_{0}$)? In general ...
0
votes
1answer
21 views

Iterative Green's function analysis for wave equation with self-driving term

I have the following wave equation: $$ (\partial_t^2 -c^2 \partial_x^2) \bar{u} = f(\bar{u}) $$ I assume I can do the Green's function method such as: $\square = \partial_t^2 -c^2 \partial_x^2$ $$ \...
1
vote
1answer
75 views

Perturbation of an object in a circular orbit

Suppose a body is moving about another body under a central force, such that the path is bounded. We can take the example for planets around the sun, and the energy is $E>0$, such that the orbits ...
1
vote
0answers
29 views

Is the quadratic stark effect on the ground state of hydrogen not $E_{100}^{(2)}=-\frac{9}{4}a_0^3\mathcal{E}^2$?

In calculating the quadratic Stark effect on the ground state of hydrogen, we find that given unperturbed hamiltonian $$H^0=\frac{p^2}{2m}-\frac{Zq_e^2}{r}$$ with pertubation $$H^1=q_e\mathcal{E}z$$ ...
1
vote
0answers
22 views

How can I understand these averages? (CMB context)

I am currently reading Prof. Mukhanov's book on "Foundations of Cosmology". In chapter 9 he is very briefly explaining free streaming and all of a sudden averages labeled with a direction ...
0
votes
0answers
12 views

Squeezing and classicalization of inflationary perturbations

Is there a simple physical picture of how/why the primordial modes (once they exit the Hubble radius) undergo squeezing and classicalize?
1
vote
1answer
50 views

Does beta decay have an explanation similar to that of the atomic transitions?

Atomic states are eigenstates of the atomic Hamiltonian. They are stationary states. Transitions from one atomic state to another are possible only in presence of an external perturbation e.g., the ...
0
votes
1answer
98 views

Doubt in expressing a solution as Fourier expansion

Goldstein 2nd ed. In its Appendix is given the derivation of Bertrands Theorem and after some steps we arrive as shown below : where it is understood the derivatives are evaluated at $u=u_0$. In ...
1
vote
2answers
35 views

Close-to-resonance driving frequency in time dependent perturbation theory

In a time-dependent perturbation theory problem, the Hamiltonian is given $H = H_0 + V$, where $V$ is a perturbation that varies sinusoidally with time. $V = V_0 \sin \omega t$. Supposed that the ...
3
votes
0answers
66 views

Can convergent perturbation series be incorrect for an action linear in the perturbation?

Non-perturbative effects are common in mathematics. For example, consider the function $$f(g) = e^{-1/g}+ g + \frac{1}{10} g^2$$ and suppose this function is the answer to some math problem. ...
0
votes
1answer
50 views

What are some good resources to learn about perturbative and non-perturbative approaches to QCD, for example Lattice QCD, at an introductory level?

I am writing at an introductory level about the anomalous magnetic moment of the muon and part of that is the subsequent Lattice QCD that potentially verifies the results from the experiments that ...
1
vote
0answers
49 views

Do Universal Spacetimes have Non-perturbative quantum corrections?

Universal spacetimes have the interesting property that their quantum corrections vanish to all loop orders, and can be viewed as classical solutions to speculative theories of quantum gravity like ...
0
votes
0answers
13 views

Choosing the positive infinitesimal in plotting the spectral function

In a recent project I have been working with spectral functions as a way to find quasiparticle energies, and I have a (perhaps rather naive) question. So let's say that we have single particle ...
1
vote
0answers
42 views

Non-periodic perturbation in solid state

I want to obtain the eigenstates of a crystalline solid with a local perturbation. In other words, I want to solve the following Schrodinger Equation: $$ H(x)=\frac{\nabla^2}{2m}+V(x)+\lambda H'(x)$$ ...
3
votes
1answer
89 views

Eigenfunctions of an Harmonic Oscillator perturbed with an Electric Field

Knowing that a particle of mass $m$ and electric charge $q$ is under an uni dimensional harmonic potential of frequency $\omega$ perturbed with and electric field $\vec{E}= E_f \hat{x} $, $\hspace{0....
0
votes
0answers
46 views

Undetermined terms in perturbative expansion of Lorentz Transformation?

I am trying to solve problem 2.1 in Schwartz, which is to derive the transformations $x \rightarrow \frac{x+vt}{\sqrt{1-v^2}}$ and $t \rightarrow \frac{t+vx}{\sqrt{1-v^2}}$ in perturbation theory. ...
0
votes
1answer
46 views

Kronecker delta on tetrad: two ways leads to two different results?

I'm new here. I'm reading https://arxiv.org/abs/1912.12469, and I'm trying to prove that \begin{equation} B \doteq 2 \delta_{a}^{\nu} [\Box E^{a}_{\nu} - \partial^{\mu}\partial_{\nu}E^{a}_{\mu}] = \...
1
vote
1answer
65 views

Why does Schwartz discard the product of counterterms $\delta_2\delta_m$?

In Quantum Field Theory and the Standard Model by Schwartz the author starts with the QED bare Lagrangian, defines $A_\mu^0 = \sqrt{Z_3}A_\mu$, $\psi^0 = \sqrt{Z_2}\psi$, $m_0=Z_m m_R$ and $e_0 = Z_e ...
1
vote
1answer
52 views

Confusion About Time Dependent Perturbation Theory

Say for simplicity we are in a two state system with a Hamiltonian: $$H=H_0+V(t)$$ Where $H_0$ is: $$\begin{pmatrix} \epsilon_0&0\\ 0&\epsilon_1 \end{pmatrix}$$ While $V(t)$ is: $$\begin{...
1
vote
1answer
46 views

Is first-order perturbation always equal to Hartree-Fock approximation?

Let us have a system of homogenous electronic system. The Coulomb interaction is given as $$ H_{int} = \frac{1}{2\mathcal{V}} \sum_{k_1 k_2 q}\sum_{\sigma_1 \sigma_2} V(q) c_{k_1+q,\sigma_1}^\dagger ...
0
votes
1answer
67 views

Perturbation theory covariant derivative

Let $\varphi$ be a scalar field and consider the metric $g_{\mu \nu}=\eta_{\mu \nu} + h_{\mu \nu}$. I want to compute $\nabla_\mu \varphi \nabla^\mu \varphi$ to first order. $$\nabla_\mu \varphi \...
4
votes
0answers
72 views

Defining the functional integral measure from the generating functional

In standard QFT we define the generating functional from the functional integral as $${\cal Z}[j]=\int\mathfrak{D}\phi e^{-S[\phi]+i\int d^Dx j(x)\phi(x)}\tag{1}.$$ On the other hand, intuitively ...
1
vote
1answer
78 views

Factorization into disconnected Feynman diagrams

I am studying "Quantum theory of many particle systems" by Fetter and Walecka, and just had my first encounter with Feynman diagrams. They are introduced to represent the terms in the first ...
3
votes
1answer
98 views

Fields with non-vanishing vacuum expectation value

In this post Arnold Neumaier wrote on necessity of vanishing vacuum expectation value if we want to have a particle interpretation of our field $\phi$: As is easily checked, fields linear in creation ...
0
votes
0answers
81 views

Deflection of a null geodesic in Schwarzschild geometry

Background In the Schwarzschild geometry the gravitational deflection of light can be described by the following equation: $\frac{d\phi}{du} = \left(\frac{1}{b^2} - u^2 + 2Mu^3\right)^{-1/2}$ , where $...
0
votes
1answer
43 views

2nd order Perturbation theory for Electron-Phonon interactions?

My understanding of perturbation theory has always been that up to second order, we can calculate the energy of a perturbed system with the following formula $$E=E_n^0+\langle n|H'|n\rangle+\sum_{m\...

1
2 3 4 5
20