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.

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125 views

Notations related to identities for spinors in the rest frame

This question pertains to some notation in Zee's QFT book, Section II.2. The Dirac equation is $$ (i\gamma^\mu\partial_\mu-m)\psi(x)=0, $$ which we can write in momentum space with the Fourier ...
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1answer
83 views

Understanding Dirac notation from matrix representation

I want to solve for the state after qubit rotation by operator, $U_\alpha = e^{i\alpha\sigma_1}$ = $\begin{bmatrix} \cos\alpha& i\sin\alpha\\i\sin\alpha & \cos\alpha\end{bmatrix}$, if qubit is ...
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1answer
36 views

Charge state in Accelerator physics

while asking for calculation of magnetic rigidity for accelerators, I am seeing notations like '238-U-28+' & '197-Au-77+ Previously I was comfortable seeing charge state like 40-Ca-1+ ions before. ...
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1answer
86 views

Confusion on repeated index for Einstein Summation

The rule for Einstein notation is that the same dummy index cannot be repeated twice. However suppose I want to compute Christoeffel symbols: $$ \Gamma^{\alpha}_{\beta\gamma} = \frac{1}{2}g^{\alpha\...
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1answer
51 views

What is the $RR$ notation in this calculation? [closed]

This is a circuit problem I am working on, and I was trying to figure out the impedance (both as a complex and real solution) of the circuit as a whole. I was looking at this tutorial and I am not ...
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1answer
120 views

Commutator of covariant derivative and field $F_{\mu \nu}$

I am working with the covariant derivative and trying to show that the commutator of this derivative $[D_\mu , D_\nu]$ is proportional to the field $F_{\mu \nu}$. That is, I need the final term to be ...
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0answers
18 views

A question about transuvection in Kerr spacetime

We know there are Killing vectors in Kerr spacetime. I wonder when doing transuvection on Killing vector, like $\left(\frac{\partial}{\partial t}\right)^\mu \bullet (dt)_\mu$ why it equals to $g_{tt}$ ...
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3answers
140 views

Commutation relation of $e^{ikx}$ and $\partial_x$ in Nakahara

I'm reading through Nakahara's Geometry, Topology and Physics and I don't understand the following derivation on pg. 41: $$ \text{Now we find from the commutation relation of } \partial_x \equiv \frac{...
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1answer
48 views

Why do the $d$ orbitals have such strange symbols?

Why are the five d-orbitals denoted by the symbols $d_{z^2}, d_{x^2-y^2}, d_{xy}, d_{yz}$ and $d_{zx}$? Does it have to do with the wavefunctions of d-orbitals? The symbols for the f-orbitals are ...
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1answer
151 views

Can I draw a variable resistor with an arrow looking to the left? What does the side the arrow look at signifiy?

Like this: Instead of this: And what does the direction that the arrow look at signify?
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1answer
48 views

What does it mean to assign group operations to distinct sets for space groups?

I am trying to understand space groups in crystallography. In Internation tables for crystallography, for a nonsymmorphic space group, they list some symmetry operations. 8 of them are listed under ...
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1answer
102 views

Proof of volume density transformation under infinitesimal diffeomorphisms using Levi-civita/ determinant

Given I diffeomorphism $x^\mu \rightarrow y^\mu = y^\mu(x) $, I want to show that the volume density is invariant, i.e. $ \sqrt{-g(x)}\,\mathrm d^4x \rightarrow \sqrt{-g(y)}\,\mathrm d^4y $. The ...
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1answer
51 views

What does '%BZ' mean in materials science?

Also, for that matter, what does k_II mean?
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1answer
211 views

Understanding the metric transformation under infinitesimal diffeomorphism

In my general relativity course, we are discussing infinitesimal diffeomorphisms defined by $x^{\mu}\rightarrow y^{\mu}(x) = x^{\mu} + \xi^{\mu}(x)$. We have been examining how different objects ...
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1answer
109 views

Einstein summation and square roots

It has occurred to me I don't know if there is a general rule about this or not. If I have an expression like: $$\int \sqrt{g_{ij}\frac{dx^i}{dt}\frac{dx^j}{dt}} dt$$ I take the summation inside the ...
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1answer
98 views

Symbols for Volt and voltage

The symbols for Volt and for voltage are both $V$. Usually, the meaning of $V$ is clear enough from context to avoid confusion. However, I find a bit odd when both $V$ appear in the same formula. For ...
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1answer
29 views

What are the superscript negative signs after the $E$ and $H$ in the equation for 'Wave impedance'?

The wave impedance is given by ${\displaystyle Z={E_{0}^{-}(x) \over H_{0}^{-}(x)}}$ where ${\displaystyle E_{0}^{-}(x)}$ is the electric field and ${\displaystyle H_{0}^{-}(x)} $ is the magnetic ...
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4answers
105 views

Why is 1000 micrometer not a correct representation of a prefix?

Why is 1000 micrometer not a correct representation of a prefix? I ask because I recently took an entrance exam with a multiple-choice question which went along the lines of which of the following is ...
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1answer
84 views

Dirac bra-ket and basis notation

I will post a image elucidating what is my doubt. I think it is more interesting to post it than to just write the equations used in the text because maybe I am losing something in the lecture. See ...
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3answers
193 views

Is $ d \mathbf v · d \mathbf v = d \mathit v^2 $?

My teacher has proved the following: $$ \mathit v^2 = \mathbf v·\mathbf v = \frac{d\mathbf r}{dt}·\frac{d\mathbf r}{dt} = \left(\frac {ds}{dt}\right)^2 \Rightarrow \mathit v = \frac{ds}{dt} $$ Because ...
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1answer
300 views

What is $D$ or $D$-with-a-slash-through-it in the Standard Model equation(s)?

In the mathematical formulation of the Standard Model, which I do not understand yet, there is a capital letter $D$ or $D$-with-a-slash-through-it that I can't find an explanation for. Flip Tanedo (a ...
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0answers
24 views

Force on an object as gradient with respect to that vector

I'm reading an introduction to molecular dynamics and I came across a particular notation for the force on the ith vector $\mathbf{r}_i$ as $$\mathbf{F}_i = -\nabla_{\mathbf{r}_i}V(\mathbf{r}_1,\dots,\...
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2answers
114 views

What does $d$ stand for in this formula?

Context: I am building a tennis ball machine and am having trouble interpreting the following formula for the flight path of the ball. I know all of the other values in the formula but the source I am ...
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1answer
209 views

Difference between $u$ and $v$ as velocity variables in special relativity [closed]

I am beginning to learn about special relativity, so I apologize for the (most likely) basic question. I frequently see, for example, the Lorentz Factor given by the equation $\gamma = \frac{1}{\sqrt{...
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2answers
1k views

Proof of the differential Bianchi identity

I was trying to prove the differential Bianchi identity by applying the covariant derivatives to each of the Riemann tensor terms $R^{\lambda}_{\sigma\mu\nu;\rho}+R^{\lambda}_{\sigma\nu\rho;\mu}+R^{\...
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1answer
104 views

Showing Lorentz force is always spacelike: Using abstract index notation

So the Lorentz force on a massive particle is given by $f^{\mu} = qg^{\mu\alpha}F_{\alpha\beta}\hat{v}^{\beta}$, where $\hat{v}^{\beta}$ is the four vector of the particle and $F_{\alpha\beta} = \...
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1answer
73 views

Radial Schrödinger equation of a scattering in two dimentions

The scattering, in two dimensions, of a particle of mass $m$ by a central potential $U(r)$. The hamiltonian of the system is $H= p^2/2m + U(r)$. Then the radial wave function $ϕ(r)$ is obtained as a ...
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2answers
145 views

Some questions about Normal Ordering in QFT

I have some questions about normal ordering in quantum field theory: I already read this very good question with very very good answers and this other question with other very good answers (I read ...
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3answers
710 views

What is meant by a partial derivative of a ket?

In my QM book I often see partial derivatives mixed with kets, like $$ \frac{\partial}{\partial a} |\psi \rangle $$ where $a \in \{x, y, z\}$. Here I'm assuming that $| \psi \rangle \in \mathbb{C}^n$ ...
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1answer
112 views

Why underscoring a letter like $\underline{F} $ for force, $\underline{\nabla} $ for the differential operator, etc, in Classical Mechanics?

In the following article: Classsical Mechanics, the letter for force $\underline{F} $, the momentum $\underline{p} $ and even nabla $\underline{ \nabla }$ are underscored. Is this a way of talking ...
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1answer
99 views

More index manipulation on Killing vectors

On the solution of problem 10.6 of the book "Problem Book in Relativity and Gravitation by A. Lightman, R. H. Price" they mention using the Killing equation: $\xi^{}_{\mu;\nu}=-\xi^{}_{\nu;\...
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1answer
60 views

Killing vector index manipulation

I was doing some problems of the book "Problem Book in Relativity and Gravitation by A. Lightman, R. H. Price" and on problem 10.14 I dont understand why they say: $\xi^{}_{\gamma;\beta}\xi^{...
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1answer
100 views

Question about an "empty ket" and Dirac's notation

This question is related to this other one and it's about Bra-Kets formalism. Hope I'm not bothering you but the truth is I'm very confused. Reading 1939 Dirac's publication on Bra-kets notation "...
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1answer
74 views

Why isn't the magnetic and electric flux, $\Phi_E$ and $\Phi_M$, typeset in italics? [closed]

In many references including Wikipedia, electric flux and magnetic flux is written as $\Phi_{E}$ and $\Phi_{B}$, respectively. But they are not vectors (even then, they have to be bold) nor units. I ...
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3answers
81 views

Navier Stokes: $(u⋅∇)u$ vs $u⋅∇u$

I can find this term stated both ways in different literature. Are they equivalent? It's weird because the dot is a dot product in (u⋅∇), but ∇u being a gradient of a vector field, would (presumably) ...
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1answer
86 views

Multiplying terms with index notation

I am trying to expand the flat-space action $$ S_{BI} = -T_p \int{d^{p+1}} \sigma \ \mathrm{Tr}\left( e^{-\phi} \sqrt{ -\det(\eta_{ab} + 4\pi^2\alpha^2 \partial_a\Phi^i\partial_b\Phi^i + 2\pi \alpha ...
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1answer
346 views

Nomenclature of X-ray transitions-Siegbahn Notation

A colleague wanted to understand the notation for X-ray transitions. The main query is about the labeling of alpha, beta and gamma, with K, L, M etc. What is the main distinguishing criterion to label ...
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0answers
43 views

Interpreting notation of tensors in QFT [duplicate]

I am having a really hard time wrapping my head around component notation for tensor fields. For example, I do not know exactly what the following expression means $$\partial_\mu\partial^\nu \phi, \...
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1answer
187 views

Raised index of partial derivative

I am having a really hard time wrapping my head around component notation for tensor fields. For example, I do not know exactly what the following expression means $$\partial_\mu\partial^\nu \phi, \...
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3answers
263 views

What does $V(r)$ mean in the Schrodinger equation?

The Schrodinger equation: $$-\frac{\hbar^2}{2m}\nabla^2\Psi(r)+V(r)\Psi(r)=E\Psi(r)$$ $$\textit{kinetic energy} + \textit{potential energy}=\textit{total energy}$$ Is one of my favourite equations, ...
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1answer
44 views

Computing derivatives "at constant" quantities in thermodynamics

What does it mean in thermodynamics when a derivative is computed "at constant $X$"? If I see $\left.\frac{\partial S(E, N)}{\partial E}\middle| \right._N$ how is the derivation performed ...
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1answer
39 views

Interpretation of Variation Notes

I would like an explanation to how this Lagragian partial derivative was taken (eq. 3). This probably is more suited for the math Stack Exchange, however this is for a physics course which is why I am ...
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1answer
145 views

Notation question for a classical field in QFT

The equations of motion for a classical field $\phi$ can be obtained using the Lagrange: $$ \frac{\partial \mathcal{L}}{\partial \phi} - \partial_\mu \bigg ( \frac{\partial \mathcal{L}}{\partial(\...
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0answers
18 views

Does $M_\odot$ go in normal text or in cursive? [closed]

The questions is just the title. I understand we're supposed to not use cursive wherever we write units (so if I write m as a variable, it goes like $m$, but if it indicates metres, then it goes as m)....
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1answer
68 views

Quantum Computing: Preparation of the Bell state Notation [closed]

I was watching some lectures on qubits. They were talking about how to generate a Bell state. They described it as follows: Prepare state 00: $$\left |0 \right> \otimes \left |0 \right>$$ Apply ...
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0answers
54 views

How a 'variation' $\delta x$ of an independent parameter differs from $dx$? [closed]

I have been reading the Classical Field theory part from The Quantum field theory book of Lewis H Ryder. After defining classical field $\phi(x^\mu)$ he says something about adding variations on both ...
2
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1answer
59 views

What does the prime symbol indicate in a nuclear reaction?

I've come across a reaction shown as $ ^7\text{Li}(\alpha,\alpha^\prime)^7\text{Li}^*$. I understand that the asterisk indicates that the final $ ^7\text{Li}$ is in an excited state, but what about ...
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1answer
35 views

Is it okay to for the integrand and bounds of integration to be functions of the same variable?

For the sake of simplicity, say we given that $a = 6t$ and that we must find the velocity as a function of time. We would set up the following integral: $$\displaystyle \int_{v(t_0)}^{v(t)}dv = \int_{...
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1answer
38 views

What does $\overset\leftrightarrow{\partial_{\mu}}$ means?

I have a scalar complex field: $\phi(x) = \phi_{1} + i \phi_{2}\;$ so $\;\phi^{*}(x) = \phi_{1} - i \phi_{2}$ where $\phi_{1}, \; \phi_{2}$ are real scalar fields. Then I have something like $\;\phi^{...
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2answers
293 views

Understanding bra-ket notation

So I am a newbie to QM, and coming from math, I believe I am not understanding some key points in bra-ket notation. So given a quantum state $\psi$, I understand that $|\psi \rangle$ is a just a ...

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