The perturbation-theory tag has no wiki summary.
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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 ...
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68 views
Time-dependent perturbation theory [closed]
I am a student looking to understand the question given in the URL.
I understand how to complete earlier parts of this question. But the part I struggle with is figuring out which are the allowed and ...
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0answers
55 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 ...
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2answers
71 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
...
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0answers
22 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 ...
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2answers
48 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 ...
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1answer
58 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) + ...
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4answers
587 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 ...
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0answers
165 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
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2answers
150 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 ...
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1answer
98 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 ...
2
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1answer
145 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 ...
1
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1answer
558 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
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2answers
391 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
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1answer
163 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
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1answer
136 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
$$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' ...
2
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1answer
103 views
Perturbation method & eigenvalues
I have a problem but I don't understand the question. It says:
"Show that, to first order in energy, the eigenvalues are unchanged."
What does it mean?
It means that if the Hamiltonian has the ...
2
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1answer
140 views
Geometric interpretation of perturbation theory in quantum field theory
I am studying GR right now, and one interesting thing I learned about vectors is that they are defined to have the same properties as derivatives.
With this in mind, can I make a differential ...
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vote
1answer
148 views
Symmetry and overlapping of ground states
In a quantum mechanics, there is the following formula to derive the zero energy $E_0$ of a perturbed Hamiltonian $$H = H_0 + V$$ knowing the zero energy $W_0$ of the free Hamiltonian $H_0$:
$$E_0 = ...
1
vote
1answer
138 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
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2answers
120 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 ...
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1answer
120 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 ...
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1answer
44 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 ...
9
votes
1answer
538 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
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1answer
121 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.
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0answers
91 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 ...
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2answers
130 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
118 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 ...
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2answers
416 views
Why is the second order perturbative correction to the ground state energy always down?
What is the physical/deeper reason for the second order shift of the ground state energy in time independent perturbation theory to be always down?
I know that it follows from the formula quite ...
4
votes
2answers
222 views
What does a non-perturbative theory mean?
I'm a science writer and I'm having difficulty understanding what a non-perturbative approach means. I thought I understood what perturbative meant, but in looking for explanations of ...
4
votes
1answer
162 views
center of mass Hamiltonian of a Hydrogen atom
I'm working through Mattuck's "A Guide to Feynman Diagrams in the Many-Body Problem", but I'm stuck on a bit which I feel should be trivial.
In section 3.2 (p 43 in the Dover edition) he gives a ...
4
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2answers
142 views
Calculating the period of a quasi-circular orbit
In solving an exercise I had to find the equation of the quasi-circular orbits of an object with the potential $V(r)=-\alpha r^{-1-\eta}$ and I expressed it as:
$$r(\phi)=\frac{r_c}{1+\epsilon ...
1
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1answer
224 views
Can't Prove formula from Sakurai's Modern QM @ Perturbation Theory
I am studying Perturbation Theory from J.J. Sakurai's textbook Modern Quantum Mechanics. I am having trouble proving formulas on page 299 (5.2.5) and (5.2.6) from the previous ones [mainly (5.2.4)]. ...
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139 views
Brillouin-Wigner perturbation theory and the useful perturbed energy
Well, when you are working with the Brillouin-Wigner perturbation theory, the corrected energy for the perturbed system, after the first order of correction, is given in terms of the unknown variable, ...
8
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1answer
299 views
Kramer's-Kronig relations for the electron Self-Energy Σ
I'm currently studying an article by Maslov, in particular the first section about higher corrections to Fermi-liquid behavior of interacting electron systems. Unfortunately, I've hit a snag when ...
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3answers
143 views
Time Varying Potential, series solution
Suppose we have a time varying potential $$\left( -\frac{1}{2m}\nabla^2+ V(\vec{r},t)\right)\psi = i\partial_t \psi$$ then I want to know why is the general solution written as $\psi = ...
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Do perturbative renormalization groups help one understand when perturbation theory can be used in general?
If, as I asked in this question, a relevant operator in a renormalization group transformation can't be used in a perturbative expansion since it becomes large as the transformations are applied, does ...
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185 views
Question about the perturbative renormalization group
I'm currently learning about the renormalization group (RG) in condensed matter physics and just want to clarify a couple of things:
When doing the RG transformation, there's a flow to a fixed point. ...
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79 views
Derivation of Brillouin-Wigner theory for coupled subpaces
I recall faintly from my quantum theory lecture that there was a really neat way to derive Brillouin-Wigner perturbation theory for the special case of two coupled subspaces that involved a geometric ...
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2answers
78 views
Nuclear physics from perturbative QFT
Is there a renormalizable QFT that can produce a reasonably accurate description of nuclear physics in perturbation theory? Obviously the Standard Model cannot since QCD is strongly coupled at nuclear ...
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2answers
89 views
In what sense are loop diagrams quantum corrections?
What's so not-quantum about tree-level diagrams?
16
votes
1answer
81 views
Asymptoticity of Pertubative Expansion of QFT
It seems to be lore that the perturbative expansion of quantum field theories is generally asymptotic. I have seen two arguments.
i)There is the Dyson instability argument as in QED, that is showing ...
4
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1answer
109 views
Convergence of quantum effective action to finite loop order
Consider the quantum effective action of a fixed QFT. If we compute it perturbatively to finite loop order $\ell$, we get a sum over an infinite number of Feynman diagrams. For example, the 1-loop ...
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4answers
445 views
Tree level QFT and classical fields/particles
It is well known that scattering cross-sections computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scaterring ...
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2answers
948 views
When can I use Wick's theorem?
Wick's theorem means that for fermions, a four point correlation function (for example) can be written in terms of two point correlation functions:
\begin{equation}
\langle b_l^\dagger b_l ...
11
votes
1answer
50 views
Limitations in using FLEX as a DMFT solver
When using the fluctuating exchange approximation (FLEX) as a dynamical mean field theory (DMFT) solver, Kotliar, et al. (p. 898) suggest that it is only reliable for when the interaction strength, ...
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2answers
308 views
Where can a good treatment of the 'sudden' perturbation approximation be found?
Where can a good treatment of the 'sudden' perturbation approximation be found?
A lot of quantum mechanics books have very brief discussions of it but I want to see it in some detail and preferably ...
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votes
2answers
438 views
Does perturbation theory break down for quantum gravity?
Perturbation theory presumes we have a valid family of models over some continuous (infinitely differentiable, in fact) range for some parameters, i.e. coupling constants. We have some special values ...
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323 views
References for ADM formalism and cosmological perturbation theory [closed]
What would you consider the best online resources for learning the 3+1 ADM formalism and gauge invariant perturbation theory in cosmology? (Assuming intermediate level GR and QFT familiarity)
