Questions tagged [interactions]
Particle interactions are changes in the nature, number, or state of several particles, usually at a specific space-time point, underlying dynamics. They are represented by special "field interaction terms" in quantum field theory and normally entail interchanges of energy, momentum, and sundry quantum numbers. They include scattering, and particle creation and annihilation.
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What is the connection between renormalizability and renormalization group classifications?
A quantum field theory can be classified as superrenormalizable, renormalizable, or nonrenormalizable and in the renormalization group an operator can be classified as relevant, marginal, or ...
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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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Why do these first-order diagrams represent "direct" and "exchange" interactions?
In Quantum Theory of Many Particle Systems by Fetter and Walecka, they perturbatively expand the fermionic interacting single particle Green's function $iG_{\alpha\beta}(x, y)$ (where $\alpha$, $\beta$...
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Can dark matter interactions create detectable shockwaves in galaxy clusters?
Suppose dark matter has weak but non-negligible self-interactions. Could colliding clusters generate pressure-like shocks in the dark sector? If so, how would these affect gravitational lensing? I'd ...
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Confusion about the running of the mass
In the Wilsonian picture one can imagine that at the intrinsic scale $Λ$ is where the "true" couplings reside and then by integrating degrees of freedom the couplings get corrected (to the ...
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Why do inequivalent representations cause a problem when defining QFT?
The way I understand it right now is:
We start off with an algebra that includes $\phi(x)$ and $\pi(x)$ and these obey the canonical commutation relations.
Then we represent these as operators on a ...
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$\phi^4$ theory lattice propagator
I'm simulating $\phi^4$ quantum field theory in real-time on the lattice.
My lattice action:
$$S=\sum_{x}\sum_{μ}η_{μμ}\frac{(\phi_{x+μ}-\phi_x)^2}{2}-\frac{(m^2+iε)}{2}\phi_{x}^2-\frac{λ}{4}\phi_{x}^...
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Why is gravity observed to be so weak? [duplicate]
The Einsteinian explanation of gravity as a distortion of spacetime caused by massive objects, often analogised by the visualisation of a rubber sheet distorted by a bowling ball placed on it made me ...
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Why a negative mass dimension of the coupling in a theory implies non-renormalizability? [duplicate]
In our lecture it was said that the reason why in QED, interaction terms of the form:
$\bar \psi \psi A_\mu^2$ do not appear is because this term has a mass dimension 5 and it would require a coupling ...
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Deriving vertex factors in Feynman rules from the Lagrangian
In the book "Quantum Field Theory" by Srednicki on page 372, the author has written the interaction terms in the scalar elevctrodynamics as follows: $$\mathcal{L}_1=ieA^{\mu}\Big[ (\partial_{...
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Next-to-Leading-Order terms in a Lagrangian
Consider a scalar field $\phi(x)$, and the following Lagrangian
\begin{equation}\tag{1}
\mathcal{L}=\underbrace{\frac{1}{2}(\partial_\mu\phi)^2-\frac{m_0^2}{2}\phi^2}_{\mathcal{L}_0}-\underbrace{\frac{...
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Sign of the minimal coupling varies in the literature
In different places the minimal coupling of quantum electrodynamics is used with different signs. For example, the wikipedia article on the Dirac equation states the covariant derivative as
$$ D_\mu \...
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How can parameters in QFT depend on scale or energy?
Often, in theoretical physics you hear things like "the coupling constants depend on the energy scale". One random example:
When this dependence on the scale is studied carefully, we find ...
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Hybridization versus renormalization
Context
Consider a Hamiltonian like
$$
H = \sum_k \epsilon_k a^\dagger_k a_k + \omega_0 b^\dagger b + \sum_k V^{(1)}_k(a^\dagger_k b + a_k b^\dagger ) + \sum_k V^{(2)}_k ( b^\dagger + b ) a^\dagger_k ...
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EFT matching at tree level
I have been studying EFT matching at tree level and a doubt came to my mind. Regarding the matching between the SM and the Fermi theory, I know that when an interaction is mediated by the W or Z boson ...
