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

learn more… | top users | synonyms

2
votes
0answers
195 views

Stationary Perturbation Theory : Estimating higher order corrections for anharmonic oscillator

Note $\hbar = 1$. $$H = H_0 + \lambda V =\frac{p^2}{2m} + m\omega^2x^2 + \lambda m^2\omega^3 x^4$$ Supposedly the perturbation expansion diverges. We are supposed to estimate for what order we have a ...
1
vote
1answer
72 views

Linear Metric Perturbation and Brans-Dicke Theory

Recently, I have been researching about modified gravity theories and one of the theories has been the theory of the graviton. If one starts with the metric tensor $g_{\mu\nu}$ and then performs the ...
7
votes
1answer
525 views

Divergent Series

Why is it that divergent series make sense? Specifically, by basic calculus a sum such as $1 - 1 + 1 ...$ describes a divergent series (where divergent := non-convergent sequence of partial sums) ...
2
votes
0answers
95 views

Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory

Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument: ... With a generalization of the argument given there (section ...
1
vote
1answer
93 views

Clarify formula in quantum perturbation theory

I'm studying perturbation theory in the context of quantum mechanics. My lecture notes say that in order to calculate the first-order correction of eigenfunction $\psi_n$, that is $\psi_n^{(1)}$, I ...
2
votes
1answer
75 views

The expansion of a function in powers of a parameter

In the perturbation theory for non-degenerate levels, the energy $E_n(\lambda)$ of an eigenstate $|\psi_n(\lambda)\rangle$ of the hamiltonian $\mathcal{H}=\mathcal{H}_0+\lambda \mathcal{H}_1$ (where ...
0
votes
0answers
83 views

QM : Perturbation theory with multiple operators

When doing perturbation theory in quantum mechanics, if the perturbation hamiltonian is made of three terms : $$W = W_1 +W_2 + W_3,$$ can I treat each term separately and performing perturbation ...
3
votes
1answer
176 views

Lagrangian density of an interacting real scalar field theory

Srednicki writes the Lagrangian density of an interacting scalar field theory as $$ \mathcal{L} = -\frac{1}{2} Z_\phi \partial^\mu \phi \partial_\mu \phi -\frac{1}{2} Z_m m^2 \phi^2 + \frac{1}{6} Z_g ...
-3
votes
2answers
172 views

The nature of theoretical models

Mathematics is exact. It is a beautiful language that allows us to express quantities that aren't possible to be represented physically. We build theoretical models of physical systems that work out ...
2
votes
0answers
74 views

QM perturbation theory : When do I have to use degenerate/non-degenerate perturbation theory?

I am considering a perturbation theory problem in quantum mechanics. The unperturbed hamiltonian is $$H_0 = A_1 \boldsymbol{B} S_{1z} + A_2 \boldsymbol{B} S_{2z}.$$ The eigenstates of the unperturbed ...
0
votes
1answer
51 views

Perturbations in arbitrary dimensions

In general is it acceptable to say that if a perturbation is in only one spatial direction then the energy eigenvalue to second order is only changed in that spatial direction? For example 3D ...
5
votes
1answer
159 views

Separation of perturbative and non-perturbative contributions in partition function computation

The following is defined, where $\epsilon \to 0^+$ is a cutoff: $$ \mathcal{F}(Z)=\int_{\epsilon}^\infty \frac{\mathrm{d}s}{s} \frac{1}{\sinh^2 s/2} e^{-sx}. $$ Question: how do we see that ...
10
votes
1answer
323 views

The Origins of Instantons from Path Integrals

I know that you can come across non-perturbative effects in QFT, particular when the coupling constant lies outside the radius of convergence of the asympototic perturbation series. From the ...
2
votes
1answer
249 views

Second order degenerate perturbation theory

What is a good resource to learn about higher degree degenerate perturbation theory - one that involves mathematics that isn't much more advanced than first order perturbation theory? I've looked ...
10
votes
1answer
399 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
4
votes
0answers
894 views

How does one actually compute the amplituhedron?

I was watching Nima's very popular talk (download if you're using chrome) (also mirrored at youtube here) about the "Amplituhedron", which has suddenly become very popular recently. He talks all ...
0
votes
1answer
314 views

Perturbation theory

I am puzzled with perturbation theory when studying quantum mechanics and solid theory. What I learn about perturbation is, from my ignorant point of view, just mathematics, or even simpler, matrix ...
1
vote
1answer
241 views

Coupled Oscillators

This is an exercise of my last exam. Since I couldn't find anybody who solved it or knows how to, it would be really nice if somebody could tell me if my thoughts on it go into the right direction. ...
2
votes
0answers
67 views

Adiabatic theorem in the regime of quantum optics

I am wondering whether there is a version of adiabatic theorem in the regime of quantum optics. My understanding of quantum optics involves with the interaction between photon and atom. This ...
1
vote
0answers
77 views

Exact summation of a sub-class of diagram: do we know the exact solved problem?

In quantum field theories (to be relativistic, (non-)relativistic statistical or whatever), we have the powerful diagrammatic approach at our disposal. Most of the time we can not sum up all the ...
4
votes
1answer
119 views

Are third derivatives of metric perturbations zero?

I'm working on a problem related to fluid perturbations of stars. I'm following this paper. They start with the Einstein equation: $$G_{\alpha \beta} = 8 \pi G T_{\alpha \beta}$$ and then perturb the ...
2
votes
1answer
237 views

Spin degeneracy in perturbation theory

In pag. 270 of Griffith's "Introduction to Quantum Mechanics" a perturbative method for finding relativist correction to the energy levels of the Hydrogen athom is exposed. It is asserted, if I ...
5
votes
1answer
175 views

How can an asymptotic expansion give an extremely accurate predication, as in QED?

What is the meaning of "twenty digits accuracy" of certain QED calculations? If I take too little loops, or too many of them, the result won't be as accurate, so do people stop adding loops when the ...
5
votes
0answers
71 views

No mixing in light cone perturbation theory

In hep-ph/0609090, Triumvirate of Running Couplings in Small-x Evolution, Kovchegov et. al. calculated the running coupling correction to the Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov and ...
2
votes
2answers
143 views

Nature of Perturbed state in Perturbation Theory?

I'm interested in the Nature of Perturbed state in Perturbation Theory. The first order perturbed state is given by $$\psi^{(1)}_{n}=\Sigma_{m}a_{m}\psi^{(0)}_{m}.$$ Where ...
1
vote
0answers
103 views

Perturbed stress-energy tensor in a cosmological context?

In the theory of cosmological pertubations, we can write the metric of a null-curvature expanding Universe as : $ds^2 = -c^2\left(1+2\frac{\psi}{c^2}\right)dt^2 + a^2 ...
0
votes
2answers
76 views

What can be the smallest chaotic system?

As I am talking about 'smallest' can I expect that it should be a quantum system? I understand that we use quantum chaos theory instead of perturbation theory when the perturbation is not small. For ...
0
votes
1answer
68 views

Why must the gravitational wave components be much less than unity?

We start with the metric tensor \begin{equation} g_{\mu\nu}(x) = \eta_{\mu\nu} + h_{\mu\nu}(x) \end{equation} in the linearised theory, or \begin{equation} g_{\mu\nu}(x) = \bar{g}_{\mu\nu}(x) + ...
18
votes
4answers
747 views

Staying in orbit - but doesn't any perturbation start a positive feedback?

I am not a physicist; I am a software engineer. While trying to fall asleep recently, I started thinking about the following. There are many explanations online of how any object stays in orbit. The ...
2
votes
0answers
351 views

Prove that the first order perturbation theory overestimates fundamental state [closed]

This was a question on my exam and I don't know how to solve it. Use the variational principle to prove that the first order perturbation theory always overestimates the energy of the fundamental ...
2
votes
2answers
398 views

proof of radius of convergence of perturbation series in quantum electrodynamics zero

Can anyone show detailed proof of why radius of convergence of perturbation series in quantum electrodynamics is zero? And how is perturbation series constructed? So, as this argument requires ...
1
vote
1answer
172 views

Energy levels in perturbation theory

Hi guys I have a quick question about perturbation theory in quantum mechanics, particularly about energy shifts. We write: $E_n = E_n^{(0)} + \delta E_n$ where $E_n^{(0)}$ is the unperturbed ...
4
votes
1answer
461 views

Scattering Processes in Scalar Yukawa Theory

I'm trying to compute nucleon-nucleon scattering in scalar Yukawa theory. Here we view a nucleon as a complex scalar field $\psi$ and a meson as a real scalar field $\phi$. They interact through ...
2
votes
3answers
1k views

Fermi's Golden Rule and Density of States

I know Fermi's Golden Rule in the form $$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$ where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition ...
5
votes
2answers
654 views

Expectation value of time-dependent Hamiltonian

I'm trying to solve a problem in QM with a forced quantum oscillator. In this problem I have a quantum oscillator, which is in the ground state initially. At $t=0$, the force $F(t)=F_0 \sin(\Omega t)$ ...
4
votes
1answer
309 views

Naive question about time-dependent perturbation theory

In time-dependent perturbation theory where $H=H_0+V$ and $V$ is considered small and has no explicit time dependence, the standard text-book treatment of the leading order probability amplitude for ...
4
votes
1answer
291 views

Scattering states of Hydrogen atom in non-relativistic perturbation theory

In doing second order time-independent perturbation theory in non-relativistic quantum mechanics one has to calculate the overlap between states $$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' ...
2
votes
1answer
197 views

Perturbation method & eigenvalues

I have a problem but I don't understand the question. It says: "Show that, to first order in energy, the eigenvalues ​​are unchanged." What does it mean? It means that if the Hamiltonian has the ...
2
votes
1answer
235 views

Geometric interpretation of perturbation theory in quantum field theory

I am studying GR right now, and one interesting thing I learned about vectors is that they are defined to have the same properties as derivatives. With this in mind, can I make a differential ...
1
vote
1answer
248 views

Symmetry and overlapping of ground states

In a quantum mechanics, there is the following formula to derive the zero energy $E_0$ of a perturbed Hamiltonian $$H = H_0 + V$$ knowing the zero energy $W_0$ of the free Hamiltonian $H_0$: $$E_0 = ...
3
votes
2answers
258 views

Diagram-like perturbation theory in quantum mechanics

There seems to be a formalism of quantum mechanics perturbation that involve something like Feynman diagrams. The advantage is that contrary to the complicated formulas in standard texts, this ...
1
vote
2answers
140 views

Most suitable metric for the Solar system?

If I wanted to solve the Einstein equations for the solar system, which choice of $g_{\mu\nu}$ and $T_{\mu\nu}$ is more suitable? I thought about using a Schwarzschild metric near each planet, but ...
3
votes
1answer
183 views

Where does this equation for a perturbed metric come from?

I'm reading an article which includes the following equation involving a perturbed metric: $$G_{AB} = \eta_{AB} + \overset{1}{\gamma}_{AB} + 2\overset{1}{\chi}_{(A,B)}\tag{4.1}$$ I don't understand ...
1
vote
1answer
75 views

Why can one equate the the zeroth order coefficient with the initial state in time-dependent perturbation theory in quantum mechanics?

Setup In the typical treatment of time-dependent perturbation theory in quantum mechanics, one arrives at the set of equations $$ i \dot{a}^{(r + 1)}_m(t) = \sum_n \langle m |H_1(t)|n \rangle e^{i ...
6
votes
2answers
399 views

Linearizing Gravity to ${\cal O}(h^3)$

I've seen the action of linearized gravity in many places. We basically have $${\cal L} ~\sim~ \frac{1}{G_N}\left( - \frac{1}{2}h^{\alpha\beta} \Box h_{\alpha\beta} + \frac{1}{4} h \Box h + {\cal ...
15
votes
2answers
1k views

Self energy, 1PI, and tadpoles

I'm having a hard time reconciling the following discrepancy: Recall that in passing to the effective action via a Legendre transformation, we interpret the effective action $\Gamma[\phi_c]$ to be ...
1
vote
1answer
186 views

What is theory of Free Energy Perturbation? How is it applicable to chemical science?

What is theory behind free energy perturbation? Is it way too difficult to understand? Can someone explain it in simple terms.
1
vote
0answers
124 views

What is better than time-dependent perturbation theory if the pointer states aren't energy eigenstates?

Time-dependent perturbation theory works excellently if the interaction is weak and the pointer states are approximately energy eigenstates. However, what if the pointer states are not remotely energy ...
1
vote
2answers
165 views

Is quantum perturbation theory taught in college?

Is perturbation theory usually taught in undergraduate physics, and how much of it is taught in quantum mechanics courses? Also, how much of quantum field theory would be taught in undergraduate ...
8
votes
1answer
155 views

What is the Principle of Maximum Conformality?

I'm trying to understand this article about an advance in the theoretical understanding of QCD which centers on the Principal of Maximum Conformality. What is this Principle? In other words, what is ...