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

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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: ...
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$\mathrm{d} \Omega_{CM}$ for a $1\rightarrow 2$ particle decay?

The differential solid angle is described in e.g. Srednicki's QFT text but only for the case of scattering. Because in the case of scattering it's defined with respect to the incoming three-momentum ...
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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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Degenerate perturbation theory applied to topological degeneracy?

Consider a quantum system described by a gapped Hamiltonian $H_0$ with degenerate ground states (GS), adding a perturbation term $V$ to $H_0$, then the low-energy physics can be described by an ...
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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 ...
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234 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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87 views

General formula to compute the redshift (first order perturbations)

Consider an expanding universe with the following metric in conformal time/co-moving coordinates: ...
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18 views

Difference between positron and electron scattering in Coulomb field

In first order of perturbation theory the S-matrix amplitude for electron scattering in the Coulomb field will be (up to normalization factors) $$ S_{fi} = \frac{iZ q^2}{\sqrt{2E_{f}2E_{i}}}\bar ...
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Why do some terms vanish in first-order perturbation theory?

In first order perturbation theory, we usually express the first order perturbation in the eigenket of the perturbed Hamiltonian in the basis of the unperturbed Hamiltonian $H_{0}$: ...
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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 ...
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62 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 ...
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55 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 ...
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150 views

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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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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Time Dependent perturbation driven at resonance

SO I am looking at driven perturbations, and I came across Fermi's golden rule here. It has a term that goes as: $$P\propto\frac{1}{\omega_{fl}-\omega}$$ Now I am curious how to go about solving this ...
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36 views

Adiabatic approximation and time-dependent problems

I am an undergraduate physics student. I have a question in approximation methods for time-dependent problems in quantum mechanics. I read the proof of the adiabatic theorem but I didn't understand ...
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58 views

What if UV behaviour of gravity was perturbative?

I understand that the UV behaviour of gravity ought to be dominated by black hole production and that graviton-graviton scattering ought to blow up above the Planck scale. Suppose, however, that ...
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41 views

Why cannot we apply perturbation theory in Born-Oppenheimer approximation

In Weinberg's Lectures on Quantum Mechanics, he mentions Unfortunately, we cannot simply use first-order perturbation theory, with $T_{nuc}$ taken as the perturbation and the state vectors ...
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39 views

How do I properly express adding perturbed states to unperturbed states?

I have a problem set due tomorrow, and the last problem is driving me nuts. Been combing through griffiths trying to find similar examples to no avail, so it'd be greatly appreciated if stackexchange ...
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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 ...
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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 ...
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81 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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111 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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Three level degenerate Hamiltonian with perturbation

I have the following system $$H=\begin{pmatrix}0&0&0\\0&0&0\\0&0&E\end{pmatrix}$$ $$V=\begin{pmatrix}0&0&\alpha^*\\0&0&\alpha^*\\\alpha&\alpha&0 ...
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26 views

What is the perturbative vacuum?

Will someone please supply me with a good definition of the perturbative vacuum vis a vis quantum cosmology?
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108 views

How explain this perturbing equation about the 43 arcseconds?

The planetary orbits have been studied as ellipses but the solar system is in motion in relation to the distant stars. Their path is along the tip of an helix and the ecliptic plane is a convenient ...
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Perturbation of a Hydrogen Atom in a Quadrupole Field

Question: A hydrogen atom is located in a quadrupole field, which gives it a perturbation $$H_1=A(x^2-y^2)$$ where $A$ is some constant. Calculate the ...
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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 ...