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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Can we deduce if a filed force is atractive in some situation from the differential cross-section?

When a beam of particles is directed against a target, the particles in the beam become scattered in different directions. The differential cross-section tries to describe this scattering: $$\frac{\...
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Is a running coupling constant a natural consequence in QFT, or is it a consequence of the "dressing-up" of particles?

The running coupling constant ("hold that constant!) is a well known phenomenon in quantum field theory. The constant varies with the energy of the interacting particles. I think this is rather ...
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Can I sum two vertices of the same order?

This is a somehow follow-up question from this one about a derivative interaction: I'll use the Lagrangian and couplings of that question, but any theory with two quartic interactions (or interactions ...
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2 votes
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D'Alembert operator interaction term in QFT Lagrangian

I'm trying to understand how to find the Feynman rules (and use them to calculate loop diagrams) for this Lagrangian (found on the Saclay lectures): $$\mathcal{L}=\mathcal{L}_\text{kin}-\frac{\tilde{...
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Scalar field mass alteration due to interaction term $\mathcal{L_{int}} = \mu^{2}\phi_1\phi_2$

With non-interactive (free) Action of two scalar fields $\phi_1$ and $\phi_2$ I add an interaction term $\mathcal{L_{int}} = \mu^{2}\phi_1\phi_2 \ \ $ i.e.: $$S = S^{free}[\phi_1, \phi_2] + S_{int} [\...
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Must the interaction of the $D$-brane be done through the closed or the open strings?

The interaction of the D brane was through the closed or open strings. However, as a distinct object, why the D brane could not have some sort of interaction themselves? i.e. an incident energy when ...
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Why is the Interaction Hamiltonian same as classical potential energy?

In the book Nonlinear Optics by Boyd, the Interaction Hamiltonian when monochromatic wave is incident is given as $$ V=-\mu E(t)= -\mu(Ee^{-iwt}+E^*e^{-iwt}) $$ I know that the classical potential ...
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If the black hole attracts photons do they do the same with respect the black hole?

If two bodies interact they interchange force carriers and as 3rd Newton law states as the one body influences the other in the same way the other body would be doing the same to the first body. So am ...
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Does the existence of exchange particles imply that that the 4 fundamental forces are delivered in discrete packets instead of continuously?

If exchange particles transfer the fundamental forces and these particles takes some amount of time to transfer this force does this mean there is a rate of force? (Side question: if two oppositely ...
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Is the definition of work related to the nature of the fundamental interactions?

I am having troubles trying to understand why is work defined as it is. So, I know how work is defined: $W = \vec{F}\cdot{}\vec{d}$ (F is the force, d the displacement) and I am okay with it. This, ...
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How does the strength of dark energy compare to the strength of the other forces?

I have read this question: http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/funfor.html So , in a nutshell, it is the fitting of data with a specific standard model that organizes the particle ...
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Polarization vector basis in Peskin & Schroeder

I am studying chapter 16.1 of Peskin & Schroeder and I am trying to understand how the chosen polarization vector basis works. It is given by the following: $$ \epsilon_i^T\cdot\epsilon_j^{*T}=-\...
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Why are hidden variables hidden?

Isn't the basic operational reason that the hidden variables are "hidden" the assumption that they can't be measured? Well in case, given that measurement is realistically speaking, nothing ...
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How is the interaction of leptons and quarks with gauge fields organized in the Standard Model?

Well, standard model has $SU(3)\times SU(2)\times U(1)$ gauge group, so this is a direct product of multiple groups embedded in larger set. So how quarks that must interact with every gauge field and ...
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Dimensional regularization vs. hard cutoff and their relation to the renormalization scale in 2d vs 4d to find $\beta$ functions

I would like to understand some shortcuts people are using to calculate $\beta$ functions using dim. reg. with mass scale $\mu$ and/or the hard cutoff $\Lambda$. My end goal is to use equation 12.53 ...
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Fundamental-ness of fundamental forces

Example : Consider a black hole and it's event horizon of radius R surrounding it . Suppose in the direction of a diameter of the black hole ( or event horizon) , there are two charged particles. ...
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Relative signs between interaction terms

What is the interpretation / meaning of relative signs between interaction terms in a Lagrangian density? (If there is none, are they even physically reasonable?) Example: Let $\phi$ be a scalar field,...
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What is the mathematical expression for the Higgs boson coupling constant?

I have been searching around and cannot get an expression for the Higg's coupling constant. By 'coupling constant', I mean for the strong force $$\alpha_S=\frac{{g_S}^2}{4 \pi \hbar c}\approx 0.1\tag{...
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Can Energy and Momentum Conservation prevent Particle Interactions?

I understand that Quantum Numbers must be preserved during particle interactions, which prevents certain interactions from occurring. However, as Energy and Momentum must also be conserved, are there ...
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What does Haag's theorem say about the Schrodinger picture?

Suppose there are two interacting fields $\phi _1 $ and $\phi_2 $. Let $\psi [\phi_1, \phi_2]$ be a functional with the two fields as the input functions and complex numbers as the output, such that ...
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Inclusion-exclusion principle in modeling interactions

When I was in school, I couldn't accept the concept of binary pairwise additive interactions, aka "Force" in classical physics. For me, the emergence of magnetism was a clue that for a 3-...
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Energy Separations in Term Scheme of Helium

I have been given the following term scheme for Helium: The bottom level corresponds to the ground state $1s^2$ term symbol while the 4 above it are the term symbols of the $1s^12p^1$ excited state. ...
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Conceptual meaning of differential cross section with respect to theta

By doing a seminar paper about Compton scattering I came across two different differential cross-sections: $\frac{d\sigma}{d\Omega}$ and $\frac{d\sigma}{d\theta}$ where $\theta$ is the scattering ...
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Is the Hamiltonian of interacting systems integrable if the interaction is linear?

Suppose we allow two integrable systems with Hamiltonians $H_1$ and $H_2$ to interact. Then their combined dynamics can be described by a joint Hamiltonian, $$H = H_1(\mathbf{q}_1,\mathbf{p}_1) + H_2(\...
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Symmetry factors in two interacting fields

Red and blue colored lines represent the two different fields. At 1st order, by the exchange of the blue legs and red legs we get $\frac{1}{4}$ factor and in one of the 2nd order term drawn above, ...
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What is $M_N$ in the Goldberger-Treiman relation?

$$g_{\pi NN} F_\pi = G_A M_N .$$ Does it stand for the magnetic moment of the neutron? One place I came across it was on Wikipedia, on their QCD Vacuum page, in the section about experimental evidence,...
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Implication and proof of conserved charge due to coupling of spin-1(massless) to spin-0 or spin-1/2

I'm following Schwartz's QFT book and problem 11.3 asks to prove that the coupling of massless spin-1 to spin-0 or spin-1/2 implies a conserved charge. It asks to refer to result from section 9.5, ...
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Dimensions of perturbative parameter in $\varphi^3$ theory?

In QFT, $\lambda\varphi^4$ is one of the most studied interactions for the scalar field. The parameter $\lambda$ is adimensional, which makes the perturbative treatment straightforward. In the case of ...
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Why is the Yukawa interaction term for Higgs coupling to quarks the way it is?

The term for Yukawa coupling between the Higgs and down quarks is given below. $$ \mathcal{L} = -(y_{e}\bar{d_{R}}\Phi^{\dagger}Q_{L}) + h.c. $$ My question is why does it take this form? Specifically,...
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Relation between source terms and interactions

I am reading the books by A. Zee and Peskin/Schroeder and in both I encountered a so called "source term" $J$, which is added to the Lagrangian as $$L(\phi) = L_{free}(\phi) + \phi(x) J(x).$$...
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Feynman vertex of an effective operator $\frac{\phi}{\Lambda}F_{\mu\nu}F^ {\mu\nu}$

Could anyone give some advice on how to calculate Feynman rule for vertex (Feynman rule of $\bar{\phi} \phi F_{\mu \nu}F^{\mu \nu}$ and its corresponding 4-photon scattering amplitude) of an effective ...
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Why Lorentzian momentum corresponds to $1/$length?

I'm reading Peskin & Schroeder's QFT, the effective coupling related with QED, is given by (7.96): \begin{align} \alpha_{\rm eff}(q^2)=\frac{\alpha}{1-\frac{\alpha}{3\pi}\log \left( \frac{-q^2}{Am^...
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31 votes
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If I push someone, what fundamental force do I create?

According to Wikipedia, all forces can be decomposed to four fundamental forces: gravity, electromagnetism, strong interaction and weak interaction. When I push someone, this generates a force. Which ...
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All forces break down into the four fundamental forces/interactions ― Is this really true?

So there is this notion that all forces can be broken down into the four fundamental forces/interactions. However, I'm starting to wonder if that is really true. The solidity of matter is explained ...
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Commutation relations interacting fields

I am reading Schwartz's "Quantum field theory and the standard model". I have a question on how he derives the Feynman rules for an interacting scalar field from a Lagrangian formalism. In ...
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Show field operator is in interaction picture [closed]

I am reading these lecture notes. In exercise 5.3 on page 7 I have to show that $$\phi(\vec{x},t)=\int\frac{d^3k}{(2\pi)^3\sqrt{2E_k}}\left(a(k)e^{-ik\cdot x}+a^\dagger(k)e^{ik\cdot x}\right)$$ is in ...
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How to identify interaction from a Lagrangian [duplicate]

In the following Lagrangian of a scalar field $\eta$, one claims that the third and fourth terms are associated to self-interaction triple and quartic coupling vertices, $$\mathcal{L} = \frac{1}{2} (\...
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How to identify interaction from a Lagrangian

In the following Lagrangian of a scalar field $\eta$, one claims that the third and fourth terms are associated to self-interaction triple and quartic coupling vertices, $$\mathcal{L} = \frac{1}{2} (\...
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Feynman rule with complex coupling

Suppose I have 3 complex scalar fields and an interaction term $$ \mathcal{L}\supset -g \chi \phi_1 \phi_2 + {\rm h.c.} $$ where $g$ is a complex constant whose phase I cannot get rid of by field ...
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Self-synchronizing and -desynchronizing systems of oscillators

There are biological systems with adaptable frequencies that are able to synchronize their frequencies, mainly individuals (see e.g. reproductive synchrony). In this case, also the phase is typically ...
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1 answer
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Current in the Dirac equation

In the Dirac Hamiltonian the current that couples with the vector potential is: \begin{equation} j^{\mu} = \bar{\psi}(x)\gamma^{\mu}\psi(x) \end{equation} However, in the non relativistic context, the ...
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How does the Higgs field decelerate particles that travel at the speed of light?

The Higgs mechanism is supposed to give mass to most particles in the standard model. The Higgs field has a positive VEV. The Mexican Hat potential is the visible expression. When the field is zero, ...
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2 votes
1 answer
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Is there a simple explanation of why coupling constants run with $\log(E)$?

The inverse coupling constants run with $\log(E)$, where $E$ is the energy or four-momentum. Some coupling constants increase, some decrease with $\log(E)$. Is there a simple argument that explains ...
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6 votes
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Why are Yukawa couplings regarded as fundamental constants if their values vary with scale?

Why are Yukawa couplings regarded as fundamental constants if their values vary slowly with the energy scale (distance scale) at which they are measured? This question is the same as why are quarks ...
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Do interactions with 2 legs (or one leg) exist in Standard Model?

Let's consider the Feynman diagram of a propagator of a particle. Is it considered as a one leg diagram or a two legs diagram? Is it considered as an interaction? (I would think that an interaction ...
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What is self-action in quantum theory?

I read that the gravitational field in any quantum theory will be self-acting. What does it mean? How can a field interact with itself?
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Why are total kinetic energy and interaction energy roughly the same for a liquid?

Let's say one has a collection of point particles, each with a kinetic energy and (e.g. Coulomb) repulsion between all of them. Under certain conditions, the system will evolve to the stable state ...
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Which 1-loop Feynman diagrams are possible from this Lagrangian interaction term?

$$ L_{int} = g \bar{L} \cdot \tilde H N $$ Where $g$ is the Yukawa coupling constant, $L$ is a lepton doublet, $H$ is the Higgs and $N$ is a right-handed neutrino. I think that at tree level only $\...
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2 answers
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Can (and should) wifi internet be considered a force? [closed]

I've recently been using my wifi internet, for the last few years and have been enjoying it very much. I am able to communicate with my family across the globe in mere seconds, it's obviously a marvel ...
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Feynman rules for non-local theory

For model with interaction: \begin{equation} H_{int} = \int f(\boldsymbol{x}_{1},\boldsymbol{x}_{2},\boldsymbol{x}_{3})\hat{\varphi}_{S}(\boldsymbol{x}_{1})\hat{\varphi}_{S}(\boldsymbol{x}_{2})\...
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