Questions tagged [notation]
This tag is for questions on the meaning, history, and usage of various symbols and notation that are used to denote different quantities in physics. Don't forget to mention the reference, where you encountered those notations.
1,576
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Expectation Value of Operator [closed]
In the book Modern Quantum Mechanics by Sakurai the expectation value of A is defined as
$$ \left <A\right> = \left<\psi\right|A\left|\psi\right>$$
And, we can also write it as (as ...
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0
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39
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Confusion about left/right-handed spinor notations
Peskin & Schroeder eq (3.78) states that
$$(\bar{u}_{1R}\sigma^\mu u_{2R})(\bar{u}_{3R}\sigma_\mu u_{4R})=\cdots$$
But I don't understand what the $u_{1R}$ means. Since 4-component Dirac spinor ...
- 21
4
votes
1
answer
275
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What is this vector notation? For linear retardance calculation
Consider:
I found this formula in https://doi.org/10.1364/BOE.426653 (NLM), a paper titled: Stokes polarization imaging applied for monitoring dynamic tissue optical clearing.
The formula is for ...
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1
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Transformations that preserve the metric [duplicate]
I know that transformations that preserve the metric (like the Lorentz transformation, or rotations) have the property:
$$S^T \eta S = \eta$$
However, I'm getting: $S^TS = I$ and I'm not sure why:
$$\...
- 1,286
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0
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Landau/Lifshitz Particle Disintegration
In Landau/Lifshitz "Mechanics", 3e., there is a problem which asks the reader to find the relation between the angles $\theta_1,\theta_2$ in the lab frame when a particle disintegrates into ...
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1
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0
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54
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What does $\overset{\circ}{=}$ mean in the context of thermodynamics? [closed]
Few days ago I started thermodynamics and whilst talking about systems and its type of walls the professor, a part from this one, showed some diagrams including this equal sign. He was talking about ...
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1
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Doubt about product of four-vectors and Minkowski metric [closed]
Given the Minkowski metric $\eta_{\mu\nu}$
And $\eta^{\mu\nu}\eta_{\mu\nu}$=4
I can write $\eta^{\mu\nu}\eta_{\mu\nu}k^{\mu}k^{\nu}$=$4k^{\mu}k^{\nu}$
But $\eta^{\mu\nu}\eta_{\mu\nu}k^{\mu}k^{\nu}$=$\...
- 1
1
vote
0
answers
25
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Meaning of adjoints for Weyl Spinors
I am going through chapter 34 of Srednicki and having doubts about Weyl Spinors. He defines
\begin{equation}[\psi_a(x)]^\dagger=\psi^\dagger_{\dot{a}}(x)\tag{1}\end{equation}
where $\psi_a(x)$ is a ...
- 1,192
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1
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Equation in Noether's paper
When I was reading the paper by Emmy Noether about the famous Noether Theorem, there is an equation I don't know its meaning and why it holds on page 5.
$$\phi\frac{\partial^{\sigma} p(x)}{\partial x^{...
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2
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1
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69
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What kind of a space is $\mathbb{C}_{-1}$?
In the first paragraph on page 24 of this paper: https://arxiv.org/abs/0904.1556, it's written
the left-handed leptons $\nu_L$ and $e^−_L$ both have hypercharge $Y=−1$, so each one spans a copy of $\...
- 318
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2
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76
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Einstein summation convention: tensor multiplication with the identity?
Suppose we have the following expression $M_{\mu\nu}\omega^{\mu\nu}$, where $M_{\mu\nu} = [M]_{\mu\nu}$ and $\omega_{\mu\nu} = [\omega]_{\mu\nu}$. Now I tell you $w = I$ with $I$ being the identity. ...
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What is $b$ in this formula of friction force?
I have seen a formula of friction force,$\vec{F}=-b\vec{v}$
I know $\vec{v}$ is velocity,but what is $b$?
Is it damping coefficient or friction coefficient?
Or damping coefficient or friction ...
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1
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1
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Graphs about four-point Feynman diagrams for $N$ scalar fields
Consider following Lagrangian for $N$ scalar fields $\phi^a, a=1, \ldots, N$ :
$$
L=\frac{1}{2} \partial_\mu \phi^a \partial^\mu \phi^a-\frac{1}{2} \mu_0^2 \phi^a \phi^a-\frac{1}{8} \lambda_0\left(\...
- 151
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1
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What symbol is used for 'proper distance'? [closed]
Proper time and proper space are generally defined as what an observer would measure in their own rest frame. If $\tau$ is a commonly used symbol for the proper time, what is the corresponding symbol ...
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Is kilo-Kelvin ($\rm kK$) avoided as it would be confusing?
When describing the colour of light globes, you see temperatures like 2700 K or 6000 K.
The surface of the sun is around 5500 K.
This could be written as 2.7 kilo-Kelvin or 2.7 kK (or 6 kK, 5.5 kK ...
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2
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1
answer
44
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Question regarding Kronecker delta [closed]
Given that, $\frac{\partial A^\mu}{\partial A^\nu} = \delta^\mu _\nu$.
How to reach $\frac{\partial A_\mu}{\partial A_\nu} = \delta_\mu ^\nu$ ?
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0
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29
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Use of Indices while deriving the Inertia Tensor
I'm trying to understand a derivation of the inertia tensor that is carried out for a rigid body rotating instantaneously about a point (the centre of mass):
$$\vec{L}=\int(\vec{r} \times \vec{v})dm=\...
- 1,580
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6
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Physical intuition of raising and lowering indices in GR
I am watching MIT open course lectures on GR https://www.youtube.com/watch?v=H6eR3sG524M&t=3614s
The lecturer introduces raising and lowering indices around 1 hour mark in the lecture.
When I try ...
- 1,171
1
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1
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Unsure of $|A \times A|$ vector notation in quantum informatics [closed]
I am new to quantum informatics and am doing a course on it. The guy who runs the course keeps writing down this notation - $|0 \times 0|$ or $|1 \times 1|$ - although it is completely foreign to me....
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Notation: Proper time as a parameter of a curve versus as a functional
I am trying to figure out some notation issues (or at least that what I assume this is).
I assume the "proper time" could refer to a "proper time functional" of a timelike path $P(\...
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1
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1
answer
85
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Notation Clarification of $G_{\uparrow\uparrow}$
I am a bit confused as to what the notation
$$G_{\uparrow\uparrow}$$
on the Green fucntions means, on a paper I have come across. Here $\hat{G}(k) = (i \omega_{l} - H_{I} - H_{P})^{-1}$.
The ...
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1
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69
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Darwin Term (Fine Structure) and the Taylor expansion of the electric potential energy
I am trying to derive the Taylor expansion for the potential $U(\vec r + \delta \vec r)$. The general expression for the Taylor expansion is: $$f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(x_0)}{n!}(x-x_0)^n....
- 1,284
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2
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59
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Simplifying Notation When Tensors are Diagonal
Is there acceptable notation to collapse sums in an expression where the tensor is diagonal? As a simple artificial example, consider the expression:
$$
F^{\alpha\beta} =g^{\alpha\mu} g^{\beta\nu} \...
1
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1
answer
77
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How does a vector field transform in quantum mechanics?
( I understand my question is a bit vague. I will try to make it more precise at the end ).
Consider a vector field $\Phi^i$ in quantum mechanics. The crux of my question is, how does it transform?
In ...
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1
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1
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28
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Difference between $\mathcal{N}=2$ and $\mathcal{N}=(1,1)$ SUSY
In supersymmetry algebra, $\mathcal{N}$ refers to $I=1,2,.. \mathcal{N} $ in $Q^{I}_{\alpha}$. My question is what does it mean to write $\mathcal{N}=(1,1)$ superalgebra?
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108
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Notation: units with negative exponents
I'm not sure if this belongs on Meta or here but:
In many scientific journals, books, and posts on this site and others, I see the negative exponent convention used for units, e.g.
$\mathrm{N} \,\...
- 8,105
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1
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What is the difference between $\partial_{\mu}$ and $\partial^{\mu}$? [closed]
I've seen in many books both expressions $\partial_{\mu}$ and $\partial^{\mu}$, which are the covariant and contravariant partial derivatives, respectively, and in one of Susskind's books he defined ...
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3
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Difference between upper and lower indices in Einstein notation
Consider a $(2,0)$ tensor $X^{\mu \nu}$ that can be represented in matrix form by:
$$X^{\mu \nu} =
\pmatrix{
a & b & c & d \\
e & f & g & h \\
i & j & k & l \\
m &...
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3
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1
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What does the $p$ in the formular $dU=Tds-pdV$ refer to?
In Callen's book (Thermodynamics and an I, second edition)p36 2.6 Based on what he said above, it seems like $p$ is the intensity of pressure inside the system.
but when I asked my friend, he said the ...
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2
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54
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Help with Commutators [closed]
I'm trying to self study quantum mechanics and am having a little trouble manipulating commutators. I get two different answers below, depending on the method I'm using. The second method gives me the ...
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1
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Simple Explanation of Electromagnetic Tensor Notation In Component Form
Can someone explain what the general concept is behind the EM tensor, as written in component form with the four-gradient? $$F^{\mu\nu}=\partial^{\mu}A^{\nu}-\partial^{\nu}A^{\mu}$$
Is that ...
2
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1
answer
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Writing a tensorial expression in differential-form notation
In six-dimensional Minkowski spacetime, if $A_{m_1m_2}$ is a rank-2 antisymmetric tensor, denoted by $A$ in differential form notation, how to show that
\begin{align}
\tfrac12 A_{m_1m_2}A^{m_1m_2}=-\,{...
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1
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2
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1
answer
84
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What does an upside down delta mean - covariant vectors? [duplicate]
I was scrolling through a wiki article on terminal velocity when I spotted an upside down delta. What does this symbol mean? How is it applied in other contexts?
EDIT: If possible could someone expand ...
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0
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What is the name and notation given to the inverse of the inertial resistivity $\beta$ (aka non-Darcy factor or Forchhiemer factor)?
The viscous resistivity $\alpha$ is the reciprocal of permeability $k$. That is, $\alpha=1/k$.
Considering the 1D isotropic non-Darcy equation,
$$\tag{1} -\frac{dp}{dx}=\alpha \mu q+ \beta \rho q^2,$$...
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3
votes
2
answers
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Difference and meaning of index the derivative operator
I'm a beginner in this type of math, we are just starting to study it, but I need some clarifications about the meaning and the difference of when we write
$$\partial_i \qquad \text{and}\qquad \...
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3
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1
answer
85
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How does the $\not{\partial}$ work in the Dirac Lagrangian?
The Dirac Lagrangian (Density) is defined in the text "Quantum Field Theory, An Integrated Approach" by Fradkin as:
$$\mathcal{L}=\bar{\Psi}\left(i\not{\partial}-m\right)\Psi\equiv \frac{1}{...
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2
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Why the $\Delta$ in the definition of pressure? (fluid mechanics)
I'm an engineering student (first year) studying Physics 1 (now an introduction to fluid mechanics).
Q1
In my physics textbook, the "medium pressure" is defined as:
$$p_m = \frac{\Delta F_{\...
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0
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20
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Understanding notation for differential mass flow rate of a control volume
Was reviewing some notes on fluid dynamics, and the notes go as follows (conservation of mass for a qubic CV),
$$\frac{dm_{out}}{dt} = \rho u (dydz)_{x+dx} + \rho v (dxdz)_{y+dy} + (similarly,forZ) = \...
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1
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56
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Quantum mechanics, Dirac notation wavefunction [closed]
How do I find $<x|p|\psi>$ in terms of $\psi (x) = <x|\psi>$
And again for $<x|H|\psi>$, where $H$ is the hamiltonian?
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2
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Applying a bra on the density operator
the density operator can be written as
$$
\rho=\sum^N _{i=1} w_i |i\rangle\langle i|
$$
Now I am not sure if the following is true
$$
\langle k|\rho|k\rangle=\langle k|\bigg(\sum^N _{i=1} w_i |i\...
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1
vote
1
answer
76
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Dynkin labels of $psu(2,2|4)$
I'm currently studying the superconformal algebra $psu(2,2|4)$, but I'm having trouble understanding its representation.
Following arxiv:1012.4004
I know that the maximal compact subalgebra is su(2) $\...
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4
answers
68
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What is the direction of $\vec r_{21}$ (position vector)? towards $\vec r_{2}$ or towards $\vec r_{1}$?
The vector representation of Coulomb's law uses a vector between the position vectors of the charges at rest. However, my teacher and a few books use the convention that vector $\vec r_{21} = \vec r_1 ...
1
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0
answers
85
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Christoffel symbol with third index up
Generally the Christoffel symbol of the first kind is defined as
$$\Gamma_{\lambda\mu\nu}=\frac12\,(\partial_\nu g_{\lambda\mu}+\partial_\mu g_{\lambda\nu}-\partial_\lambda g_{\mu\nu}) \tag{1}$$
and ...
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1
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49
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Invariance of continuity equation for Galilei transformations
I want to prove that the continuity equation for fluids, $$\dfrac {\partial \rho}{\partial t} + \nabla \cdot (\rho \textbf{u}) = 0$$ is invariant by Galilei transformations. My attempt:
Using index ...
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1
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1
answer
127
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Valid Tensor equation
Let us have the equation as;
$A_{{\mu}{\nu}}$$B_{\mu}$=$C_{{\mu}{\nu}}$ , $\mu$ and $\nu$ are free indices.
Is the above equation a valid tensor equation? If not then what correction should be made to ...
1
vote
1
answer
89
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What does this notation mean in a nuclear reaction?
$$\rm ^9Be (\alpha, n) {}^{12}C$$
What does this notation mean in a nuclear reaction?
1
vote
1
answer
51
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Square notation for Lagrangian terms
I am starting field theory and have questions regarding what I learned about tensor/Einstein notation. I made up my own problem where I am deriving things backwards to practice tensor notation and ...
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0
votes
1
answer
79
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Differentiating the index notation
I am always confused with the algebra of differentiating the index notation, and have browsed many other posts but still confused. There must be details I have been missing. It would be really ...
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-2
votes
1
answer
45
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What are these two equations related to Maxwell-Boltzmann Distribution called? [closed]
I have come across these two equations on Maxwell-Boltzmann Distribution:
and
May I please know what the equations are called so I can read up more about them?
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