Questions tagged [perturbation-theory]
Perturbation theory refers to methods for understanding physical systems by treating them as small modifications to exactly solvable systems.
1,367 questions
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Gauge dependent mass definition in perturbation theory
Let's say we describe an unstable particle using perturbation theory. Then we have a non-zero decay width, which we say $\Gamma$. Now, if we define mass to be the pole of the propagator, we get
$$
\mu^...
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What is the point of the "Polarization Insertion" in many-body theory?
In Fetter and Walecka's Quantum Theory of Many-Particle Systems, after a discussion of Dyson's equation for the single particle Green's function in spacetime ($x$) and momentum/frequency ($k$; for ...
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Numerical results of precision tests in perturbative QFT
Where can I find a database or tables with the precisions/contributions that each Feynman diagram term adds to most common and famous numerical estimations for the standard model of particles (like $g$...
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Is there any general principle for why small deviations in models give only small errors in predictions?
I have a question regarding the pragmatic heuristic that goes something along the lines of
"Small deviations from reality in a model yield small errors in the predictions of the model"
Is ...
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In what sense is "momentum" flowing in Feynman diagrams?
Given a Lagrangian $\mathcal{L} = \mathcal{L}_0 + \mathcal{L}_I$, we can construct the Feynman diagrams for some process by writing out the Taylor series for our interaction term and judiciously ...
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Understanding derivation of quantum differential scattering cross-section [duplicate]
I've been trying to understand quantum scattering, but I think I am not very clear about the full picture in the derivation of differential cross-section below. In Modern Quantum Mechanics by Sakurai, ...
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First-order time-independent perturbation on Bloch states subject to near-uniform magnetic field
I am a student currently trying to re-derive the results discussed in this paper (https://doi.org/10.1103/PhysRevLett.99.197202) on deriving an expression for orbital magnetisation using 'standard' ...
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When is the 3D Dirac delta function a good approximation for scattering?
When discussing X-ray or neutron scattering, it is usually assumed that the scattering potential is of the form
$$V_{\mathrm{eff}}(\mathbf{r}) = \sum_i b_i \delta^3(\mathbf{r}-\mathbf{r}_i)$$
with $...
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Adiabatic evolution of the free vacuum in QFT
In the context of the pertubative expansion of Green's functions in Quantum Field Theory, it is a pretty standard trick to assume the free and interacting Hamiltonian are conected via adiabatic ...
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Partial waves in QFT: Why only $l=0$ modes contribute for $\varphi^n$ like interactions, and for derivative interactions we also have $l \ne 0$?
Some context
In these notes on AdS/CFT by Jared Kaplan (section 8.1) on pg. 70-71, he tries to derive anomalous dimensions from basic quantum mechanics and the idea is simple: We are doing ...
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Correlation functions in perturbative QFT
In perturbative quantum field theory, one starts with interaction Lagrangian density
$$\mathcal{L} = \mathcal{L}_{\text{free}}+g\mathcal{L}_{\text{I}}\tag{1}$$
Where $g$ is coupling strength. ...
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Computing the ground state energy using perturbation theory?
I know that, in quantum statistical mechanics, the ground state energy of a system at finite temperature can be computed from the partition function:
$$Z_{\beta} = \sum_{n=0}^{\infty}e^{-\beta E_{n}} =...
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Making sense of perturbation theory in many-body physics
I am trying to teach myself perturbation theory in the context of many-body quantum mechanics. I must say I am facing some difficulties in understanding the motivations and ideas behind the method, ...
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Understanding frequency and frequency integration of Green's function
The single particle Green's function is defined by:
$$
G(\mathbf{k}, t) = \langle \Psi | \mathcal{T} c_{\mathbf{k}}(t) c_{\mathbf{k}}^{\dagger}(0) | \Psi \rangle
$$
The physical intuition behind this ...
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How to obtain $ϕ(a)$ to solve a multi-scale matter density contrast equation in cosmological perturbation theory?
I have derived the equation for the evolution of the matter density contrast $\delta_M(a)$:
$$
\delta_M''(a) + \left(\frac{4}{a} + \frac{H'(a)}{H(a)}\right)\delta_M'(a)
+ \frac{3 \phi'(a)}{a}
- \frac{...
