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.
159
questions with no upvoted or accepted answers
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Formatting of quark fields
I try to follow the ISO 80000-2 norm when typesetting physics. This is more a typesetting question but I did not want to ask this at the TeX SE site since this only applies to physics and I am not ...
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4
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0
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What decides the signs and coefficients of terms in superfield?
I'm working on a problem in 3d field theory and I'm confused about how to write the superfields. Specifically, I'm not sure if the signs and coefficients of terms are purely a matter of convention or ...
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votes
1
answer
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Dot convention inductors in series: what is going on
So I'm really confused with mutual inductors and dot convention. If your answer is going to be a link to any website I can assure I read them all and that only left me more confused. So here are my ...
3
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What is $\mathrm{U(1)}$ vector and axial?
In hadron physics we talked about $\mathrm{U(1)_V}$ (vector) and $\mathrm{U(1)_A}$ (axial) as well as $\mathrm{SU(3)_L}$ (left) and $\mathrm{SU(3)_R}$ (right). There are certain relations between them ...
- 8,301
3
votes
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Topological quantum computation : Anyon model
Could someone tell me about Frobenius-Schur indicator and the associated cups and caps notation in context of anyon model. One possible reference could be Parsa Bonderson thesis which is freely ...
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3
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0
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Group theory notation used in physics (AdS/CFT)
This in the context of the AdS/CFT correspondence. I am reading this review on AdS/CFT Aharony et. al. (The MAGOO review) The abstract can be found here
Equation (2.50) of the above paper lists the $...
- 22.9k
3
votes
1
answer
698
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Nuclear state notation $J^\pi$
I have learned from nuclear physics literature that a nuclear state can be denoted as $J^\pi$, where $J$ is the spin and $\pi$ is the parity, such as $0^+, 1^+$. But when I read some papers on nuclear ...
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2
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129
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Thermodynamics Chain Rule And Independent Variables
I was reading my textbook and I came up across the entropy $S(T,V,N)$ where temperature $T$, volume $V$, and number of particles $N$ are the independent variables. According to the chain rule the ...
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2
votes
0
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110
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Marginalisation of a joint probability distribution in bra-ket notation
Given a wave function $\Psi(\vec r_1, \vec r_2)$, where $\vec r_1$ and $\vec r_2$ are the positions of particle 1 and 2, respectively, the probability of finding particle 1 at position $\vec r$ (...
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2
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What do $<111>$, $[010]$, $(111)$, and $\{100\}$ represents for a cubic crystal lattice?
I want to know the difference between different notations in crystal lattice. I know what Miller indices are but what does these four different notations really mean.
2
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Why do we have momenta $k_\pm=k_x \pm i k_y$ in $k\cdot p$ models instead of $k$?
The Hamiltonian for a simple 2-band model after $k\cdot p$ is:
$H(k)=\begin{bmatrix}
\frac{E}{2}+\frac{\hbar^2 k^2}{2m} & \frac{\hbar}{m}k\cdot P \\
\frac{\hbar}{m}k\cdot P & -\frac{E}{2}+\...
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answers
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Notation of basis functions for irreducible representations
In character tables for symmetry groups, there are typically basis functions for each irreducible representation given. There are basis functions given like $xy$, $S_x$ or $R$. Could someone explain ...
- 171
2
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0
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Notation for the vector space of (real) classical solutions
I am aware that this might not be the best place to ask, but I can't say I know of any other better alternative so I apologize in advance. I'm following Wald's book on QFT in curved space-time and I ...
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2
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0
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130
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Indexes in the Gaussian functional integral
This is a question spawning from a comment made to my previous question. There I was asking about taking some functional derivative in the effective action of the non-linear sigma model. The comment ...
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2
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1
answer
116
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Understanding Einstein Summation in the Geodesic Equation
I am trying to teach myself general relativity. I believe I do not fully understand Einstein summation. I have two versions of the same question
Non-relativistically: If $V^μ= ů$ (the velocity) ...
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2
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0
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701
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Notation for vectors and covectors
This is probably a very simple question, and I think I know the answer, but I cannot find a place to solidly confirm this.
So if I want to write a vector $\mathbf{V}$ in terms of its contravariant (...
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2
votes
0
answers
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What is the origin of the naming convention for the various branches in vibration-rotational spectroscopy?
In vibration-rotational spectroscopy, the different spectral lines are grouped into branches for different changes in the total angular momentum, i.e.
$$
\begin{array}{rrrrrr}
& \mathrm{O} & \...
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2
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0
answers
60
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Vibrational quantum notation
Reading articles on spectroscopy I often see this notation:
30001 <- 01101, 00011 <- 00001
in context of molecular ...
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2
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0
answers
169
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Convention in physics for [],{} and operators (QM)
I got a little mixed up with the convention in physics.
Usually a hat means an operator. For a given electron-ion Hamiltonian
$\hat{H}_{e-n}$, what are the difference between these:
1) $\hat{H}_{e-...
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2
votes
2
answers
134
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Index transposing in Einstein notation
When working with Einstein's summation convention, how do I have to transpose the indexes of the tensor?
For example, suppose I want to take the matrix product with its transpose. Which is the correct ...
2
votes
1
answer
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QCD color factors from quark gluon vertices
The color factors in QCD tell us the relative strength of the coupling of a quark emitting a gluon, a gluon emitting a quark-antiquark pair or a gluon emitting two gluons. To calculate let them we ...
user17574
1
vote
0
answers
65
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Christoffel symbol with third index up
Generally the Christoffel symbol of the first kind is defined as
$$\Gamma_{\lambda\mu\nu}=\frac12\,(\partial_\nu g_{\lambda\mu}+\partial_\mu g_{\lambda\nu}-\partial_\lambda g_{\mu\nu}) \tag{1}$$
and ...
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1
vote
1
answer
47
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Square notation for Lagrangian terms
I am starting field theory and have questions regarding what I learned about tensor/Einstein notation. I made up my own problem where I am deriving things backwards to practice tensor notation and ...
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1
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0
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73
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Clarification of Notation in MTW's Gravitation, Section 6.4
Three difficulties concerning notation in MTW's Gravitation Section 6.4, which introduces a coordinate system for an accelerated frame:
the time axis e0' is the observer's 4-velocity, so he is always ...
1
vote
0
answers
57
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Is there a way to rewrite all of circular motions in exterior algebra?
The torque is defined as the cross product between the position vector and the applied force:
$$\tau = \vec{r} \times \vec{F}. $$
The cross product only works in 2 and 3 dimensions and the ...
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1
vote
1
answer
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Question regarding Energy Interaction of two particles
https://imgur.com/s6RGUKb
To give a context as to what I'm asking here ,I am talking about the energy of a two particle system (section 4.9 Taylor's Classical Mechanics) .
My question is what does $\...
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vote
0
answers
56
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Non-minimally coupled inflation — expansion
In the Wikipedia article on "Inflaton" there appears the following formula:
$$S=\int d^{4}x \sqrt{-g} \left[\frac{1}{2}m^2_{P}R-\frac{1}{2}\partial^\mu\Phi\partial_{ \mu }\Phi-V(\Phi)-\frac{ ...
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1
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0
answers
110
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Index-free notation indulgence!
I have been try to find as an exercise for myself the most suitable coordinate-free form of the following equation found in Misner, Thorne, Wheeler's Gravitation (p. 84)
\begin{equation}
v^\ell = (F_{...
- 85
1
vote
0
answers
64
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Identity $\nabla_{j}\partial_{i} = \Gamma ^{k}_{ij} \partial_{k}$ involving covariant derivative
I am trying to understand the identity i have came across, but i am not being able to:
$$\nabla_{j}\partial_{i} = \Gamma ^{k}_{ij} \partial_{k}$$
I thought that such equality would become obviously if ...
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1
vote
1
answer
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Convective derivative N-S
This is probably an easy answer, but I've not been able to find it yet -
Why in some formulations of the N-S equations (for example here https://www.grc.nasa.gov/www/k-12/airplane/nseqs.html), is the $...
- 11
1
vote
0
answers
57
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How should second differentials and differentials of one-forms be expressed?
Components with under-barred indices are expressed on a covariantly constant basis. This is equivalent saying the under-barred coordinates lie in the tangent plane. Basis vectors are written in the ...
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1
vote
1
answer
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Covariant derivative with an upper index in terms of Christoffel symbols
I have encountered expression
$$\frac{1}{2}\left(2 \dot{g}_{\mu}{}^{\lambda ; \mu}-\dot{g}_{\mu}{}^{\mu ; \lambda}\right)$$
in a GR paper.
Here we assume to be working with the de Sitter metric $g$ ...
- 1,032
1
vote
0
answers
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The Euclidean vector momentum operator in spherical coordinates
I am having some trouble with the notion that the different components of a vector operator can be hermitian in one coordinate system but non-hermitian in another. I have seen e.g. Bra-ket notation in ...
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1
vote
0
answers
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Understanding an integral from Quantum Field Theory
In Eberhard Zeidler's Quantum Field Theory I: Basics in Mathematics and Physics, under section 11.6.4 - Integration tricks, the following integral which is then evaluated using a Schwinger ...
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1
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0
answers
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Matrix multiplication in Feynman's paper on quantum mechanical computers
In a paper by Feynman, on how to embed a Turning machine in the ground state of a many-body quantum system, a product of two matrices is defined (equation 1). This product does not appear to have the ...
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vote
2
answers
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Understanding the bra-ket antilinear correspondence
I can't follow how the above argument leads to (1.8).
I am able to prove it only if I can show $$\langle a | c\rangle+\langle b| c\rangle=(\langle a|+\langle b|)\,|c\rangle$$
But I don't understand ...
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1
vote
1
answer
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Noether's theorem derivation by Greiner
I'm reading Quantum Mechanics (Symmetries) by Greiner, in the topic of Noether's theorem (pp. 6-7) there are points where it is a little bit confusing. I'll add a link to the google book version so as ...
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1
vote
0
answers
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Significant figures in scientific notation
If I want to express a number in scientific notation, e.g. 0.0068
according to my textbook this is $$6.8 \times 10^{-3}$$
I'm wondering would $$68 \times 10^{-4}$$ be equivalent? 0.0068
has got two ...
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1
vote
0
answers
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Unequal forms of the Yang-Mills equation in local coordinates
I found three different expressions for the Yang-Mills equation in local coordinates:
In 1: $\square A^{\beta}-\partial^{\beta}\left(\partial_{\alpha} A^{\alpha}\right)+\partial_{\alpha}\left[A^{\...
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1
vote
1
answer
64
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How do you express the rate of change with radius of an expression $x$, at a given radius in a gravitational field?
Is it enough to say $dx/dr$, and specify an expression that x refers to, or do you need also to say something like (dx/dr)(r), because it is at a given radius?
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0
answers
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"$10^{\mathrm{th}}$" Index skipped in M-theory
Why is it that in M-theory, the 11-dimensional vectors are labelled with indices $0 \dots 9,11$. For example, the spatial momentum components are $p_{1}, \dots, p_{9}, p_{11}$. Why is the $10^{th}$ ...
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vote
2
answers
122
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Inverse of a metric tensor on a Hermitian manifold
Let $(M, g)$ be a Hermitian manifold. We have a metric tensor $g^{i \bar j} dz_i \otimes d\bar{z_j}$, where $(g_{i \bar j})$ is a hermitian positive definite matrix. Now we naturally get the inverse ...
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1
vote
2
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Finding the new force of vectors
It's been a while since the last time used vectors. I came across with the following question.
Find the Net force (size and orientation) of the vectors
$$
\vec{A}=15,37^{\circ},\,\vec{B}=5,162^{\...
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1
vote
1
answer
129
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Confusion about expressing an inner product using the Einstein summation convention
I think this likely comes down to the following expression,
$$g’^{ab}e’_a e’_b = \delta ^a_b $$
Is this in agreement with the Einstein summation convention? Because even though the two indices are ...
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1
vote
0
answers
81
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The mathematical structure of $\widehat{su(2)}_k$
Some of my colleagues work on CFT's and quantum groups and I hear them talk a lot about $\widehat{su(2)}_k$ algebras. According to them (and the general physics literature) these are what ...
- 1,286
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0
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113
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Where does this alternative form of Faraday's law come from?
In the Sears-Zemansky physics book on page 1007, there is an alternative way to express Faraday's law for a moving conductor in a magnetic field:
$$d\mathcal E =\left(\vec v \times \vec B\right)\cdot ...
1
vote
0
answers
147
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How to understand notation in "Introduction to Quantum Mechanics (3rd Edition)" by David Griffiths, Chapter 3.6.2?
In the 3rd edition, on page 118, the projection operator is introduced as
$$\hat{P}=|\alpha\rangle\langle\alpha|.$$
Then Griffiths says that when $\hat{P}$ acts on another vector, it looks like ...
1
vote
0
answers
29
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Different between index locations on tensors
My question is in regard to the position of upper and lower indices on tensors, specifically in this case I am considering position 4-vectors and the Minkowski matrix.
On the Wikipedia page I see ...
1
vote
0
answers
78
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Notation in a question on probabilities and particle counting
I'm working through Stephen Barnett's book on quantum information and have come across the following question (1.5, for anyone keeping track at home)
A particle counter records counts with an ...
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0
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170
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Most used convention about Christoffel symbols
Just a simple question: what is the most used form for Christoffel symbols, (1) or (2), see below:
(1) $$\Gamma_{ij}^{k} = g^{kl}\Gamma_{lij}$$
and then, we have: $$\Gamma_{lij}=\Gamma_{lji}$$
(2) $...
user87745