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.
1,541
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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 ...
- 31
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0
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13
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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,
$$\tag{1} -\frac{dp}{dx}=\alpha \mu q+ \beta \rho q^2,$$...
- 1,275
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0
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58
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Units inside square brackets [closed]
As a physics teacher, I often see students writing a physical quantity with a numerical value followed by its unit (sometimes not...) placed inside square brackets.
We can argue about the meaning of ...
3
votes
2
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65
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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
$$\partial_i \qquad \text{and}\qquad \...
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2
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1
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How does the $\not{\partial}$ work in the Dirac Lagrangian?
The Dirac Lagrangian (Density) is defined in the text "Quantum Field Theory, An Integrated Approach" by Fradkin as:
$$\mathcal{L}=\bar{\Psi}\left(i\not{\partial}-m\right)\Psi\equiv \frac{1}{...
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1
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2
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76
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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:
$$p_m = \frac{\Delta F_{\...
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0
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18
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Understanding notation for differential mass flow rate of a control volume
Was reviewing some notes on fluid dynamics, and the notes go as follows (conservation of mass for a qubic CV),
$$\frac{dm_{out}}{dt} = \rho u (dydz)_{x+dx} + \rho v (dxdz)_{y+dy} + (similarly,forZ) = \...
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0
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18
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Explanation of name Cobimaximal Matrix
Cobimaximal matrix is a modified form of the neutrino mixing matrices and it is consistent with neutrino oscillation data. It predicts atmospheric mixing angle to be 45 (degree) but new oscillation ...
-1
votes
1
answer
55
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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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1
vote
2
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50
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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
$$
\langle k|\rho|k\rangle=\langle k|\bigg(\sum^N _{i=1} w_i |i\...
- 13
1
vote
1
answer
54
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Dynkin labels of $psu(2,2|4)$
I'm currently studying the superconformal algebra $psu(2,2|4)$, but I'm having trouble understanding its representation.
Following arxiv:1012.4004
I know that the maximal compact subalgebra is su(2) $\...
- 33
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votes
4
answers
59
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What is the direction of $\vec r_{21}$ (position vector)? towards $\vec r_{2}$ or towards $\vec r_{1}$?
The vector representation of Coulomb's law uses a vector between the position vectors of the charges at rest. However, my teacher and a few books use the convention that vector $\vec r_{21} = \vec r_1 ...
1
vote
0
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66
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Christoffel symbol with third index up
Generally the Christoffel symbol of the first kind is defined as
$$\Gamma_{\lambda\mu\nu}=\frac12\,(\partial_\nu g_{\lambda\mu}+\partial_\mu g_{\lambda\nu}-\partial_\lambda g_{\mu\nu}) \tag{1}$$
and ...
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1
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30
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Invariance of continuity equation for Galilei transformations
I want to prove that the continuity equation for fluids, $$\dfrac {\partial \rho}{\partial t} + \nabla \cdot (\rho \textbf{u}) = 0$$ is invariant by Galilei transformations. My attempt:
Using index ...
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vote
1
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92
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Valid Tensor equation
Let us have the equation as;
$A_{{\mu}{\nu}}$$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
87
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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
47
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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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votes
1
answer
72
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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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votes
1
answer
43
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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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2
votes
2
answers
115
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Question on Lie algebra indices, spinor indices and gamma matrices indices in QCD and QED lagrangians
The question is written in section $2)$
1) Introduction
1.1) QCD
For a non-abelian group, the connection term on the lagrangian will be written as
$$\mathcal{A}_{\mu}=A_{\mu}^{a}T_{a}\tag{1}$$
This ...
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1
vote
1
answer
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Derivation Dirac equation
In introduction to elementary particles by David Griffiths p.227, Griffiths says that
$$(\beta^kp_k + mc)(\gamma^{\lambda}p_{\lambda} -mc) = \beta^k\gamma^{\lambda}p_kp_{\lambda} - mc(\beta^k - \gamma^...
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1
answer
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Why do we use $\Delta m$ in the derivation of angular momentum of a rigid body?
while I was watching a derivation of angular momentum of a rigid body on youtube, it came to my attention that the person who was doing the derivation, used $\Delta m$. my question is, why did he use ...
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1
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Transformation of Yang Mills Field Strength
I am confused about the expression $$F_{\mu \nu} \to F_{\mu \nu}' = U F_{\mu \nu}U^{\dagger}.$$ I found related Phys.SE posts How would one show that a nonabelian field strength tensor transforms in a ...
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3
answers
98
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Clarifying Bra-Ket Notation: Orthonormal Bases
I was asked to find the trace of $(A \in M_{n \times n})$, the matrix that can be written in the form:$$A=\frac{1}{n} \sum_{r, \, q \, = \, 1}^n (-1)^{r+q}|r \rangle \langle q| \quad ,$$ where {$|r \...
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1
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337
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Can someone explain this Feynman Diagram in the picture?
I don’t understand this diagram at all, and what is the meaning of the $g$?
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Question on the indexes of the lagrangians describing gauge theories
For a gauge group $SU(3)_{C}$ we can construct its principal and associated bundles; we can introduce spinor fields via spin structures and spinor bundles and so on, arriving in a lagrangian theory ...
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vote
1
answer
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How to express symmetry of a mixed (1,1) tensor with upper and lower index?
In the context of general relativity, I am working with the energy-momentum tensor $T$, which is a rank-2 tensor whose components are usually denoted by $T^\mu_{\ \ \ \ \nu}$. However, I am unsure of ...
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Evaluating the commutator of derivative and position [duplicate]
In Zettili's book on quantum, the fully worked problem 2.6 asks to show
$$
\hat{A} = i(\hat{X}^2+1)\frac{d}{dx} + i\hat{X}.
$$
Is Hermitian. Where $\hat{X}$ is the position operator. I took the ...
0
votes
1
answer
45
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Notation to give units in legend/axis label/etc
When writing e.g. an axis label for a plot or a header for a table column that contains data that is associated with a unit (e.g. a length in meters), I always used to write it down like this:
...
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vote
2
answers
96
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Why is time harmonic follow the form of $e^{-i\omega t}$, not $e^{i\omega t}$? [closed]
In physics, when we solve an PDE or ODE, the solution usually has the form of
\begin{equation}
f=C_+e^{i\lambda x}+C_-e^{-i\lambda x}
\end{equation}
and the "causility" will eliminate one ...
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votes
2
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53
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Unclear passage, autoket and eigenvalues
I am not understanding a passage that our professor wrote: those are the lines.
$e_0 \cdot \hat\sigma$ is an operator, whose eigenvalues are $\pm 1$. He applied this to a ket $|e_0, \pm 1 \rangle$:
$$...
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0
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Meaning of Left-Right Arrow in a Fitting Formula [duplicate]
I initially posted this question on Astronomy Stack Exchange but the site seemed rather inactive so I will try to ask it again on Physics, hopefully it doesn't go against any rules.
I was reading this ...
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2
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140
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Minkowski inner product
I'm elementary in physics and I have a question about a notation. In the book, the author says that the rotation group is the set of linear transformations on $\mathbb{R}^n$ preserving the inner ...
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2
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How do I understand the Hodge $⋆$ operator in Yang-Mills Lagrangian?
The gauge-invariant part in Yang-Mills Lagrangian is
$$
\mathcal{L}_{\text{gauge}} = -\frac{1}{2}TrF_{\mu\nu}F^{\mu\nu} = -\frac{1}{4}F_{\mu\nu}^aF^{a, \mu\nu}.
$$
Sometimes I see the lagrangian ...
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2
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99
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A question about a comment from Byron and Fuller, pg 533
Seeing the equation,
\begin{equation*} (\hat{A} -\lambda)G_\lambda
(\mathbf{x},\mathbf{y})=\delta^{(3)}(\mathbf{x}-\mathbf{y}) \tag{1}
\end{equation*}
in the answer
What is different between ...
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votes
3
answers
52
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Planck constant imaginary instead of imaginary PDE coefficients in the Schrödinger equation
Trying to get a first understanding of QM. The Schrödinger equation in standard form for $\Psi$
$$ i \hbar\frac{\partial }{\partial t} \Psi(x,t)
=\left[-\frac{\hbar^2}{2m}\frac{\partial^2 }{\partial t^...
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votes
1
answer
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Notational meaning of $\nabla_{\lambda}V^{\rho}$ and $\nabla_{\mu}\nabla_{\nu}V^{\rho}$
This question is related to Reconciling different expressions for Riemann curvature tensor, but it's different since it asks for some notational clarification arising out of calculations I did. To not ...
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1
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$\nabla$, $\cdot \nabla$, $\nabla \cdot$, $\nabla^2$ - What do they do? [closed]
I'm trying to teach myself Smoothed Particle Hydrodynamics. Unfortunately, my background is in electronics, so the Navier Stokes equations are somewhat alien to me, as is vector calculus. The video I'...
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Bianchi identity contradiction in Abelian case
In non-abelian gauge theory, such as P & S's chapter 15, eq. (15.89), we also have Bianchi identity.
Start with
$$\epsilon^{\mu\nu\lambda\sigma}[D_\nu,[D_\lambda,D_\sigma]]=0$$
and use $[D_\mu,D_\...
- 1,287
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1
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Taking a function out from between a bra- and ket-vectors in the general case
I had a guestion on what kind of functions can one pull out of braket-term. For example I know that
$$
\langle{\psi_1}|c|\psi_2\rangle = c\langle{\psi_1}|\psi_2\rangle, \hspace{0.5cm} c\in \mathbb{C}.
...
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0
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How to interpret $\int\mathrm{d}^2z$? [duplicate]
In chapter 6 of Tong's lecture notes on string theory when calculating the Virasoro-Shapiro/4-point Tachyon amplitude he arrives at the integral
\begin{align*}
C(a, b) = \int\mathrm{d}^2z\ |z|^{2a-2}|...
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3
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98
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Harmonic Oscillator Eigenket Notation
I'm reading the $3^{\mathrm{rd}}$ edition of Sakurai and Napolitano's Modern Quantum Mechanics, and I have a brief question about the notation used to describe the eigenstates of the harmonic ...
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0
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62
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What is $\vec{q}$ in this expression?
So I am having trouble following and understanding what $\vec{q}$ is in this evaluation. Here is my attempt at a solution:
Since the solution is for 2P to 1s transition it must be in the form of ...
2
votes
1
answer
86
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Four-vector and Notation significance [closed]
As the title suggest, this has to do, on the most part, with four vector notation. I have a series of questions, the majority, related to this topic:
1- If we assume a lorentz boost in the x direction ...
- 1,208
2
votes
2
answers
59
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Trace and index manipulation
Imagine that I have a quantity $F_{ab}$ multiplying the stress tensor $T^{ab}$:
\begin{equation}
F_{ab} T^{ab}.
\end{equation}
There is also a metric, say $h_{ab}$. If I want to write the above ...
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1
vote
1
answer
71
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Position of an index when raising and lowering indices
I'm reading Carroll's book on GR, page 25, and have a question about raising and lowering indices in 1.72:
For the first equation, why do we have (sorry I don't know how to leave spaces for the lower ...
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2
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130
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How does one write Adjoint, Self-adjoint and Hermitian operators in Dirac notation?
The following portion is paraphrased from Mathematical Methods for Physics and Engineering by Riley, Hobson, and Bence.
The adjoint of a linear operator $\hat{A}$, denoted by $A^\dagger$, is an ...
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1
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33
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Why are $K_{\alpha}$ and $K_{\beta}$ emissions denoted by $\alpha$ and $\beta$?
Perhaps this is a silly question, but is there any reason for the labelling of $K$ emissions as alpha and beta? From what I know, all $K$ emissions relate to an electron transition down to the $n=1$ ...
- 87
1
vote
0
answers
99
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What does this notation mean in a many-body quantum system? [closed]
I'm studying the Many-body quantum system with the textbook Many-Body Quantum Theory in Condensed Matter Physics written by Henrik Bruus and Karsten Flensberg, and right now I'm feeling hard to ...
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votes
1
answer
115
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What is the symbol to differentiate between 3D and 4D tensors?
I am writing a computer program and in there I need to differentiate 3D tensors (metric tensor, Riemann tensor, Ricci scalar, Christoffel Symbols, etc.) from 4D ones.
I wanted to write something like $...
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