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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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Question about pion EFT interaction with the proton [closed]

I have encountered the following Lagrangian describing the interaction between pions and some nucleon N $$\mathcal{L}=\frac{F_{\pi}}{4}Tr(∂_{\mu}U^{\dagger}∂^{\mu}U)+\bar{\psi}_{L}i\not\partial\psi_{L}...
Filippo's user avatar
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What does it mean to "resum" the large logarithms?

I am struggling to understand the concept of resummation of large logarithms in QFT; from what I learnt so far the problem relies on the fact that if a full theory defined in the UV contains much ...
Filippo's user avatar
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Understanding Virtual Particles and the Mediation of Forces

When trying to understand how the electromagnetic force works in a Quantum-Mechanic context (what mediates it), one concept you will quickly encounter is that of virtual photons (and more generally ...
Giorgos G's user avatar
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Feynman rule for scalar QED vertex

A popular problem in QFT textbooks and courses is to derive the Feynman rules for scalar QED. Usually, this theory is presented via the following Lagrangian density: $$\mathcal{L} = (D_\mu\phi)^\...
Rafael Grossi's user avatar
2 votes
1 answer
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Why do heavy bosons have less range?

Why is it that there's a precise relationship between the mass of a mediator particle and its range? Because mass shouldn't directly affect decay time, right?
Flamethrower's user avatar
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1 answer
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Is the scalar field in the Yukawa interaction real or complex?

Consider a theory containing a Dirac field $\psi$ and a scalar field $\varphi$ where the only interaction is given by a Yukawa potential $$ V = -g\bar{\psi}\varphi\psi $$ I know that real scalar ...
paulina's user avatar
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4 votes
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116 views

Interpretation of self-interacting terms in the expansion of a pure YM Lagrangian?

Let $A^{\alpha}_\mu$ be the gauge field of a Yang-Mills theory where $\alpha$ is the gauge index of generators for some Lie algebra with structure constant $C_{\alpha \beta}^\gamma$ and $\mu$ is the ...
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Do coupling constants change under length rescaling?

I am studying renormalization in the Skinner's notes https://www.damtp.cam.ac.uk/user/dbs26/AQFT/Wilsonchap.pdf and I can't understand the passage in formula (5.22) $$\Gamma^{(n)}_{\Lambda}(x_{1},...,...
Filippo's user avatar
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Electrostatic Self-energies of Non-uniformly charged bodies

Consider the figure given above. A semicircular ring of radius $R$ and mass m carries non uniform linear charge density $λ=λ_o\sin\theta$. A rod of mass $m$, length $2R$ and uniform linear charge $λ_o$...
DarkKnight's user avatar
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What is the difference between field and disturbance?

In my textbook Sears & Zemansky's University Physics, 15th ed, Page-399, it is written that, "A useful way to describe forces that act at a distance is in terms of a field. One object sets ...
Peter swift's user avatar
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In a scalar QFT, how are Feynman diagrams drawn if the interaction Lagrangian has multiple terms?

In my introductory course for QFT we have covered many different interaction Lagrangians using scalar fields, for example $\phi^3$ theory. However, so far we've only covered Lagrangians with a single ...
agaminon's user avatar
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Why are the equations of motion for a free quantum field theory always linear?

So far all the Lagrangians I have come across in my studying of quantum field theory have had a free theory whose equations of motion are linear. A linear free theory is of course desirable from a ...
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Can you model relativistic interactions without locality?

Assume $c=1$ I've been doing relativity by myself so I may be making some assumptions here that I would not have if my learning had been more extensive. One such assumption is that you can model the ...
NaiDoeShacks's user avatar
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How can interacting field operators in $2D$ still satisfy the canonical commutation relation?

Free fields in any dimensions are well-known to be Gaussian, act on the Fock space and satisfy the canonical commutation relations. By definition, interacting field operators are NOT such cases, as ...
Keith's user avatar
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3 votes
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Does a massless boson imply an infinite interaction distance?

As we know, if we use the Lagrangian of electrodynamics we can find that the photon has no mass. If the photon had mass, it would even have 3 polarizations, which is a consequence of having mass. My ...
LEON LOPEZ EMMANUEL's user avatar
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Unification of Interactions

It has been asked before but with a different aim, and was answered mathematically, while I look for a practical understanding of it. If the Four Foundamental Forces were unified in the first instants ...
FringesExplorer's user avatar
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Observation without interaction thought experiment [closed]

Here I am going to talk about a thought experiment that I have thought There is some isolated place in the universe where there is no EM field other than the field created by a moving point charge ...
Physics's user avatar
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3 answers
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Triviality of $\phi^4$ theory, is it settled now (2024)?

According to the answer on question 364576 this should be settled. But after looking for clear statements of the current situation on triviality of $\phi^4$ theory, I'm still not sure, because: In ...
Jos Bergervoet's user avatar
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1 answer
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Why is $\frac{1}{2}\delta_Z(\partial_\mu \phi_r)^2 - \frac{1}{2}\delta_m \phi_r^2$ treated together in Feynman diagrams?

From P&S consider the $\phi^4$ bare Lagrangian: $$\mathcal{L} = \frac12 (\partial_\mu \phi)^2 - \frac12 m_0^2\phi^2 - \frac{\lambda_0}{4!} \phi^4.\tag{p.323}$$ When using renormalized perturbation ...
CBBAM's user avatar
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Calculation of Vertex factor from Lagrangian

I am studying spontaneous symmetry breaking of a complex scalar field $\phi(x)$ of a global $U(1)$ symmetry: $\phi(x)\to e^{i\alpha}\phi(x)$, where $\alpha$ is a real constant. I am considering the ...
Anant Badal's user avatar
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1 answer
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If "borrowing energy for a short time" interpretation of HUP is wrong, then how are the ranges of fundamental forces explained?

I have heard many people mention that heisenberg uncertainity prinicple doesn't really allow 'violation of energy conservaiton for a short time'. i.e, virtual particles, are just a mathematical tool. ...
Luffy curious's user avatar
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Long and short range correlations in nuclear physics

In the introduction of chapter 6 of Ring and Schuck's book "The nuclear many-body problem" it is stated that "the Hartree-Fock method partially takes into account the particle-hole part ...
OutrageousKangaroo's user avatar
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How to treat the processes involving propagators of two particles that mix with each other?

Consider a Lagrangian with two scalar particles $V,A$: $$ L =L_{\text{kin}}(V)+L_{\text{kin}}(A)+g_{VA}VA. $$ It looks to me that I can treat the $VA$ term either as a mixing term, diagonalizing the ...
Name YYY's user avatar
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6 votes
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Periodic boundary conditions: torus or infinite images?

I have a "philosophical" question regarding the use of periodic boundary conditions (PBD) in modeling and simulating systems of particles. Let us consider a system of $N$ classical particles ...
Michele Pellegrino's user avatar
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1 answer
62 views

How to correctly interpret $\hat{\sigma}_{eg}^i \hat{\sigma}_{ge}^j$?

I am trying to figure out the paper of Asenjo-Garcia et al.: PHYS. REV. X 7, 031024 (2017). Specifically, in e.g. Equation (5): $$ \mathcal{H}_{eff} = -\mu_0 \omega_0^2 \sum_{i,j = 1}^N \mathbf{D}^* \...
Emil Henningsen's user avatar
2 votes
1 answer
154 views

Deriving Feynman rules for scalar QED

I am a bit confused about Matthew D. Schwartz's statement of the Feynman rules in scalar QED (chapter 9, section 9.2 titled Feynman rules for scalar QED. The Lagrangian is \begin{equation} \mathcal{L} ...
QFTheorist's user avatar
1 vote
1 answer
32 views

Determining force of interaction from a decay equation

I have the decay equation $$p + π^− → n + K^− + π^+.$$ I have been told the force of interaction in this is the weak nuclear force, but I was looking for an explanation of how you can work that out ...
Techwizard's user avatar
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How scalar field couples to the $B$-field in Dilaton-Gravity-Maxwell action?

Given the following $d$ dimensional dilaton-gravity-Maxwell low-energy effective action in the target space of a bosonic string: $$S=\frac{1}{2\kappa^2}\int d^dx\sqrt{-G}e^{-2\Phi}\left[R-\frac{1}{12}...
Daniel Vainshtein's user avatar
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1 answer
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Understanding changes in surface charge distributions between high and low $\sigma$ resistors and the relationsship to Drude's model

I am thinking about ohms relationship $E = j\sigma$, where $\sigma$ is entirely material-dependent, which can be explained by Drudes model and the common explanation that surface charges create the E-...
Niclas's user avatar
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1 answer
110 views

Quantization of an Interacting Field Theory

The procedure to quantize free field theories is imposing a commutation/anticommutation relation with the field and its conjugate momentum, as $$\mathcal L = i\bar\psi\gamma^\mu\partial_\mu\psi\...
vfigueira's user avatar
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0 answers
157 views

Fermi Golden Rule: Why interaction picture is fundamental for proving it? [closed]

Sakurai and Wikipedia proove the golden rule in the interaction picture. As the reason of that choice is not clear for me, I ask you what are the difficulties that rise up when you try to get the rule ...
Grande Rocco's user avatar
2 votes
1 answer
110 views

Schrodinger's picture and Heisenberg's picture in finding interaction ground state and two-point correlator

In section 4.2 of An Introduction to Quantum Field Theory by M.E.Peskin and others, it derives interaction ground state by observing the time evolution of ground state in free field theory (pg.86), ...
Ting-Kai Hsu's user avatar
1 vote
0 answers
82 views

Diagrammatic derivation of the Dyson–Schwinger equation

I am following chapter 9 of the Rammer's book on Field Theory (which you can find here: https://www-thphys.physics.ox.ac.uk/talks/CMTjournalclub/sources/Rammer.pdf). I am referring to section 9.2.2, ...
Ruth Murphy's user avatar
1 vote
1 answer
83 views

Why do ( within my limited understanding.) Energy and matter act in opposite ways [closed]

I would like to preface this by stating this type of research is my hobby not my profession. If I understand the basic explanation correctly, energy tends to spread out evenly within a closed system ...
TylerTheSparky's user avatar
3 votes
1 answer
120 views

Explict Form of Ground State in Interacting Field Theory

In An Introduction to Quantum Field Theory by Peskin and Schroeder chapter 4, it has discussed about the ground state $|\Omega\rangle$ (where $|0\rangle$ is the ground state in free field theory) in ...
Ting-Kai Hsu's user avatar
1 vote
1 answer
79 views

What is screening in Quantum Field Theory and how does it influence the strength of interactions in QCD?

Question is fairly straight to the point. In particular, how does it influence the strength of particle interactions?
Mike Mutethia's user avatar
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2 answers
135 views

How do the Spin Angular Momenta and Orbital Angular Momentum of Neutron and Proton couple to result Total Angular Momentum of Deuteron=1?

In the book "Introductory Nuclear Physics" by Kenneth S Krane, it is written that "there are four ways to couple $s_n$, $s_p$, and $l$ to get a total $I$=1" for Total Angular ...
Lusypher's user avatar
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2 votes
1 answer
137 views

2-point correlation function between two different fields

Suppose we have a lagrangian $\mathcal{L}$ made by different fields, i.e. \begin{equation} \mathcal{L}= \mathcal{L_0} + g\phi\partial_\mu\phi A^\mu, \end{equation} where $\mathcal{L_0}$ is the free ...
Alex's user avatar
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0 votes
0 answers
107 views

What is the difference between interaction energy and self-energy?

From my understanding self-energy is the energy required to put charges in a certain charge distribution and interaction energy is the potential energy caused by the interactions between particles, ...
randomdude's user avatar
2 votes
0 answers
81 views

Why Fock representation holds only in a free quantum field theory?

With a quantum system with $N$ degrees of freedom, all the representations are unitarily equivalent to Fock representation. However, if the number of degrees of freedom goes to infinity, there are ...
MBlrd's user avatar
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1 vote
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Beta function of two copies of the same model with interactions

I have a particular model with two couplings, let's call it model A, for which I have the set of beta functions and fixed points. Now I am interested in a model where I have two copies of model A, ...
dorrel's user avatar
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0 answers
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Difference between Dicke superradiance and dipole-coupled emitter superradiance

This question is similar to "What causes the collective emission in Dicke Model?", but more specific. I wonder if the situation described in [1] R. H. Dicke – Coherence in Spontaneous ...
A. P.'s user avatar
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1 vote
3 answers
100 views

Interactions within constituents of dark matter

Inspired by Are the visible matter and dark matter separately segregated? I wonder if the constituents (I don't say particles, as we don't know) have actions and forces among themselves, that we ...
Gyro Gearloose's user avatar
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1 answer
105 views

Can any Hamiltonian be expressed as a sum of free and pair-interaction terms?

Consider a number of systems $\{S_i\}$ with a Hilbert space $\mathcal{H}=\otimes_i\mathcal{H}_{S_i}$. Consider an arbitrary Hamiltonian $H$ defined on this Hilbert space. Can this arbitrary ...
Pol's user avatar
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0 answers
31 views

When does a theory decouple?

The question is very broad, but it seems to me that the term 'to decouple' is also used in various contexts. For example, neutrinos decouple from the photons in the early Universe, when the ...
kalle's user avatar
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80 views

How to evaluate interaction term in Hamiltonian?

If one has an interaction term in the Hamiltonian of a system as follows:$$ \sum_{\vec{q}}V(\vec{q}) \psi(\vec{k}-\vec{q}) $$ where $\psi(\vec{k}-\vec{q})$ and $V(\vec{q})$ is the wave function and ...
L_J's user avatar
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4 votes
1 answer
174 views

Is the notion of particles dependent upon the Hamiltonian being quadratic?

I am studying interacting QFT in the context of quantum fields in curved backgrounds, and I am getting some confussion about the concept of particles. To study some gravitational phenomena involving ...
TopoLynch's user avatar
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9 votes
1 answer
213 views

Free higher spin fields and gravity

There are soft theorems that suggest that any massless boson with spin higher than 2 should be a free field theory and cannot have interactions. Does this mean that one cannot embed such fields into a ...
Panopticon's user avatar
1 vote
0 answers
77 views

What exactly are the categories of intermolecular forces

So I read the wikipedia and its catagorization is somewhat vague. (Link here: https://en.wikipedia.org/wiki/Intermolecular_force) In wikipedia, the van der waals forces are quite clearly stated to ...
aaa's user avatar
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1 answer
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${}$Higgs mechanism

Is is correct to say that, elementary particles have different masses, because they have different coupling strengths to Higgs field? And if yes. Does it make sense to question, why they have ...
Arjun Bindra's user avatar

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