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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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 ...
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Why isn't energy conserved in time-ordered diagrams?
I'm new to particle physics, and I'm reading chapter 5 of Prof. Mark A. Thompson's "Modern Particle Physics", which talks about Time-ordered perturbation theory vs QED. However, in page 119 he wrote:
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How can I see where this formula for a general vertex factor comes from?
I have been reading Srednicki from the beginning and doing all the exercises, and I hit a big roadblock at Q10.4, as I can't seem to figure out what Srednicki is doing in his solution. Luckily, I ...
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Feynman rules for Gross-Neveu (four fermion) model
I'm having hard times in finding the Feynman rules for the Gross-Neveu model in two dimensions:
$$ \mathcal L = \bar \psi^i (i \gamma^{\mu} \partial_{\mu} ) \psi^i + g^2 (\bar \psi^i \psi^i )^2 \; ,$$
...
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What is the intuitive physical difference between fermions and hard-core bosons?
(This is a soft question.)
If we work on a discrete lattice for simplicity, then ordinary bosons are characterized by creation and annihilation operators that satisfy the canonical commutation ...
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Is the Weak Force really a force?
My definition/understanding of a force still carries largely over from classical physics which is something that tends to change the motion of an object (a push, pull). Gravity and electromagnetism ...
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Coincidence of spacetime events & Lorentz invariance
Am I correct in thinking that if two spacetime events are coincident in one frame of reference, then they are coincident in all frames of reference, i.e. coincidence of spacetime events is a Lorentz ...
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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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Issues of infinity with time ordering of the interaction Hamiltonian of $\phi^4$ theory
I use $\phi^4$ theory as an example here, but similar things happen to other theories as well.
In $\phi^4$ theory, we can easily use the Lagrangian here to write down the interaction Hamiltonian (in ...
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Deriving the Lagrangian of a set of interacting particles only from symmetry
In section 5 of Landau and Lifshitz's Mechanics book, they show that the Lagrangian of a free particle must be proportional to its velocity squared, $\mathcal{L} = \alpha\mathbf{v}^2$ using only ...
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Feynman Rules from Lagrangian with charge conjugation matrix
I'm dealing with a doubly charged scalar singlet that interacts only with the
right-handed muon as follows,
$$\mathcal{L} = \lambda \psi_{R}C\psi_{R} \phi^{++},$$
where $\lambda$ is the coupling, $\...
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Is the phrase "coupling constant" interchangable with " strength of interactions"?
Can I use the terms coupling constant and strength of interactions, interchangeably, or are there more subtleties to the term coupling constant that I am not aware of?
Coupling Constants from ...
user81619
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How to prove that identical particles are attracted or repelled in a given spin-s interaction theory?
Let's assume that we have integer spin interaction theory (EM field, linearized gravity, arbitrary gauge spin s theory). How to prove the consequence that in interaction theory with spin $s = 2n$ two ...
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Physical meaning of minimal coupling assumption
In SM, both for the gauge field $A_{\mu}$ associated with photon and for the gauge fields $W^{j}_{\mu}$, to restore the invariance of the lagrangian after the changing of the global transformation to ...
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How do quantum fields really couple?
The term "coupling" between quantum fields refers to certain terms in the Lagrangian (density) $\mathcal{L}$ where the respective field operators appear together, e.g. $g\phi^\dagger\psi $ with ...
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Coupling spin 3/2 fields with electromagnetism (causally)
I am trying to read literature regarding the coupling of massive spin-$\frac{3}{2}$ fields with electromagnetism. Apparently, an elementary (i.e. not composite) massive spin-$\frac{3}{2}$ field can't ...
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Feynman rules of Non-Abelian gauge fields
The Lagrangian of Non-Abelian field is:
\begin{equation}
\mathcal{L} = -\frac{1}{4}[\text{quadratic term} + 2gf^{abc}A_{\mu}^{b}A_{\nu}^{c}(\partial^{\mu}A^{\nu a}-\partial^{\nu}A^{\mu a})+ \text{...
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Is it valid to add energy densities of *interacting* perfect fluids?
In several papers on interacting perfect fluids in cosmology, the authors assume that we still can add the energy densities and pressures of the individual fluids, as if there wasn't any interaction:
\...
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Number of possible Feynman diagrams at a given perturbative order
In perturbative quantum field theory, all amplitudes for processes $\sum \text{in}\to \sum \text{out}$ involving particles that interact according to a certain interaction Lagrangian $\mathcal L_I$ ...
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Constraints on scalar field theories in $n$ dimensional spacetime
Let us consider the classical action in $n$-dimensional (flat Minkowski) spacetime
$$
S=\int dx^0\ L=\int d^nx\ \mathcal{L}\tag{1}
$$
with Lagrange function $L$ and Lagrange density $\mathcal{L}$.
For ...
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In matter-antimatter interactions, what's the meaning of "touch"?
In this question, the top answer gave a seemingly good description of the particle interaction, but what exactly the interaction is seemed to be left unstated.
I've only the most rudimentary ...
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Scattering in QM/NRQM vs QFT
As discussed in this question: How does a wave packet get scattered? And shown in, for example, this video: https://www.youtube.com/watch?v=iq4lGVznr_8
In quantum mechanics particles are scattered due ...
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Asymptotic states in strongly-coupled QFTs
In QFT the asymptotic states play a very important role, as they are the basis on which we decompose our in-states and out-states when we calculate correlation functions.
However, I have not been ...
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A superficially divergent diagram in $\phi^4$ interaction, rarely appeared in the literature
I'm studying superficial degree of divergence of Feynman diagram and I am confused about some concept.
In particular, its scope is on scalar $\phi^4$ interaction in $3+1$ dimension.
Some literature ...
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Chemical potential and interactions
I'm interested in a model with interactions between different kinds of particles. Each particle species has its own chemical potential.
I want to treat the system in the Matsubara formalism. Here, to ...
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Can interacting quantum field theory describe more than just scattering?
From my understanding we do not yet know how to make much out of interacting QFT other than scattering amplitude at asymptotic infinity. (Correct me if I misunderstand.) But path integral, in ...
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Clarifications on the assumptions made for QFT interactions
I am reading about scattering and S-matrix in the context of quantum field theory and although I understand the math and the physical interpretation of the final results, I am confused about some ...
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Renormalization group in time and space, finite size systems
I have few questions about RG. For completeness and clearness I'll start more or less from the beginning.
Initially I have bare two-point propagator:
\begin{equation}
G_0(r)=\frac{1}{r}
\end{...
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Interaction terms in the curved space Lagrangian
Apologies in advance if this has been posted before, I've browsed through the questions but couldn't find anything similar.
I've been studying some QFT in curved space (mainly using the Birdell & ...
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Mixture of two fluids: Is that EoS possible and how to interpret it?
In the context of cosmology, a perfect fluid is generally described by an equation of state (EoS) of the following form:
$$\tag{1}
p = w \rho,
$$
where $p$ is the fluid's pressure and $\rho$ is its ...
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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 ...
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Self-coupling of gravity
From the EInstein eqn it is obvious the metric field couples to itself since $R_{\mu\nu}$ is derivative and multiplication of $\Gamma$'s.
Some GR textbooks explained this coupling as necessary from ...
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How to update $SU(2)$ Higgs fields with Heat Bath algorithm?
I'm trying to update the Higgs field coupled with a pure gauge $SU(2)$ theory through Heat Bath algorithm. Pure gauge and Higgs configurations should be updated separately. For the pure gauge part the ...
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Ward Identity, Green Function with Current Insertion and Amputated Green Function
The QED Lagrangian (for one fermion) is:
$$\mathcal{L} = -\frac{1}{4}F_{\mu \nu}F^{\mu \nu} + \bar{\psi}\left(i \gamma^{\mu}\partial_{\mu} - m \right) \psi - q \bar{\psi} \gamma^{\mu}A_{\mu}\psi = \...
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What is really meant by a nearest neighbor interaction?
Suppose there are three harmonic oscillators, which are spacially separated forming a chain where there are interactions only between nearest neighbors.
$$\require{enclose}
{\scriptstyle \enclose{...
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Why right-handed neutrino?
Interacting part of the $SU(2)_L$describing the Higgs and fermionic sector with one family
$$\mathcal{L}= \bar{l}_Li\not Dl_L+\bar{e}_Ri\not\partial l_L+ \bar{\nu}_Ri\not\partial\nu_R - (y_{\nu}\bar{l}...
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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 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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General Method for Calculating Excluded Volume
In section 5.3 of Kardar's Statistical Physics of Particles, the van der Waals equation is given as:
$[P+\frac{u_0 \Omega}{2}(\frac{N}{V})^2][V-\frac{N\Omega}{2}]=Nk_BT$
The van der Waals parameters ...
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Cluster Expansion and Partition Function for a Collection of Interacting Particles in Presence of an External Potential
I was watching a lecture on statistical mechanics (link here) in which the instructor explains the statistical mechanics of weakly interacting gas molecules (no external potential) using the standard ...
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Calculating the path integral for cubic interactions (perturbatively)
I'm trying to apply the Coleman-Weinberg mechanism to the weakly interacting, $g \ll 1$, $\mathbb{Z}_2$-symmetric $\phi^6$-theory in $d = 3 - \epsilon$ dimensions (in Euclidean signature)
\begin{...
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Degeneracy of Atomic energy levels
I've started reading about the atomic spectra and came across LS coupling and so on. However, I have a doubt regarding the entire thing.
Let us say, we have 2 electrons, say $4p-4d$ state, and we are ...
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What is the difference between $L_1+L_2$ and $L_1 \cdot L_2$ in spin-spin coupling?
Consider two spin systems $\mathcal{H}_1$ and $\mathcal{H}_2$, each with spin operator $L_1$ and $L_2$, respectively.
What is the difference between $L_1+L_2$ and $L_1 \cdot L_2$?
As far as I ...
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Connection between the Haag and the Currie-Jordan-Sudarshan (CJS) no-go theorem
The Currie-Jordan-Sudarshan (CJS) no-go theorem states, that in the setting of Hamiltonian mechanics, if the particle coordinates $q_i^{\alpha}$ (on the trajectory) transform correctly under the ...
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Is $\phi^4$ theory unstable?
I tried to write a simulation of a $\phi^4$ theory for 2+1 dimensions. But whatever values I gave for the coupling constant it always seems to blow up.
i.e. a wave-like equation with a mass and ...
user84158
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Treating a mass term as an interaction
The mass term of, say, a one real scalar free quantum field theory can be treated as an interaction with $$\mathcal{L}_I= -\dfrac12 m^2 \phi^2.$$
Once that diagrams are summed to all orders of ...
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How to imagine wavefunction branching?
This is a question particularly geared toward the Many Worlds interpretation, but I think it could be translated to other approaches as well.
I am not sure I understand exactly what sort of events ...
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About the diagonalization of non-linear (in fields) actions
Suppose we have some interacting theory with the action:
$$
S = \int d^{D} x \left(\partial_\mu \phi \partial^\mu \phi + V(\phi)\right)
$$
Where $V(\phi)$ is a potential (some polynomial of degree $&...
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Interaction vertex in non-commutative QFT
If $\hat{S}_{1}=i \int d^{d} x \mathcal{L}_{I}$ and
$$
\begin{aligned}
V\left(x_{1}, x_{2}, \ldots, x_{n}\right) & \equiv \int\left[\prod_{j=1}^{n} \frac{d k_{j}}{(2 \pi)^{d}}\right] e^{i k_{\mu}^{...
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$2 \to 2$ scattering cross section in arbitrary theory
What is the general method to compute the $2 \to 2$ scattering cross section given an arbitrary Lagrangian ? I would like a step by step recipe that can be easily implemented in Mathematica.
For ...
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