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

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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 ...
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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 ...
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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 ...
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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 $F(t)=F_0 \sin(\Omega t)$ ...
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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 ...
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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' ...
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224 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 ...
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256 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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269 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 = ...
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274 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 ...
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147 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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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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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 ...
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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 ...
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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 ...
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195 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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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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168 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 ...
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160 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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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 ...
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573 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 ...
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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 ...
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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 ...
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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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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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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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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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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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222 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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291 views

In what sense are loop diagrams quantum corrections?

What's so not-quantum about tree-level diagrams?
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243 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 ...
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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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Time-Dependent Potentials in Quantum Mechanics

A potential that depends on time is usually solved using the time dependent perturbation theory in standard undergraduate textbooks in quantum mechanics. The reason usually mentioned is that time ...
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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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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 ...
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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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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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Perturbation theory with degeneracy even after 1st order

Most textbooks on basic quantum mechanics tell you that when your initial Hamiltonian $H_0$ has degenerate states, then before you can do (time independent) perturbation theory with a perturbation ...
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Is string theory over a time varying background a conformal field theory to all orders in perturbation theory?

When computing the first order perturbative corrections to string theory over a curved background, we find the background has to be Ricci-flat if the dilaton is constant and we have no fluxes. Such is ...
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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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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)