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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42 views

$\frac{\partial x_{\mu}}{\partial \omega_{a}}$ doesn't make any sense

In the book Condensed Matter Field Theory by Altland, on page 32, it is given while explaining Noether's theorem that To understand the impact of a symmetry transformation, it is fully sufficient to ...
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54 views

Notation confusion for differential volume

Can anyone help me with an explanation of the following notation. I am a bit confused: Lets say we have some type of integral and in the end we write different differential, such as: $$d\vec r ,\quad ...
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Symbol of quintal

Depending on the source, I have come across the symbol of quintal as 'q', 'qt'and 'qtl'. Is there a standard symbol for quintal. If yes what is it?
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81 views

What is Dirac indices?

In Maggiore A Modern Introduction to Quantum Field Theory Eq. 4.31 $$\{\Psi_a(\vec x,t),\Psi_b(\vec x,t)\}=\delta^{(3)}(\vec x-\vec y)) \delta_{ab}$$ where "$a,b=1,2,3,4$ are the Dirac ...
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What is $v_{\infty}$?

So, you can calculate the trajectory of a celestial projectile by using this equation: $$e=\frac{rv_{\infty}}{\mu},$$ where $\mu$ is the central body's Gravitational Parameter, so it is definable by $\...
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1answer
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How to express the elementary work definition as an explicit functional expression [duplicate]

My assumption here is that in the definition of elementary work : $dW = F ds$ symbol $d$ represents a differential. But a differential implies a function : $dy =_{df} d[f(x)] = f'(x) \Delta x = f'(...
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1answer
66 views

Can anyone expound this Projectile Motion computation please?

I have this formula for projectile motion that I'm using in Unity game engine for getting the low or high Velocity of a projectile depending on how close or distant the target is (as long as it is ...
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2answers
69 views

How does the tranpose conjugate of an operator act on a bra and a ket in the context of annihilation and raising operators?

Consider the annihilation and raising operators as follows: $$\hat a|n\rangle=\sqrt{n}|n-1\rangle\qquad\text{and}\qquad\hat a^\dagger|n\rangle=\sqrt{n+1}|n+1\rangle$$ I know normally if I have an ...
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54 views

Raising and lowering indices in line elements - why do we raise and lower them in line elements?

My question refers to Piattella's lecture notes on cosmology. On page 15, the Euclidean line element is defined as $$ ds^2 = \vert d\mathbf{x}\vert^2 = \delta_{ij}dx^idx^j. $$ My first question is ...
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What does the star mean in $\rightarrow ZZ^{(∗)}$? [duplicate]

What does the star mean in $\rightarrow ZZ^{(∗)}$? Z boson can neither be positive nor negative. "For masses above 130 GeV, Higgs-boson decays, H $\rightarrow ZZ^{(∗)}$, where each Z decays to a ...
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63 views

Contraction of antisymmetric tensor [closed]

Let $\omega^{ab}$ be antisymmetric in the indices $a$ and $b$. Why we have $$\omega^{ab}(\theta_{ab}-\theta_{ba})=2\omega^{ab}\theta_{ab}$$
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81 views

What is $\mu_5$ in string theory?

I have come across the quantity $\mu_5$ in string theory quite a lot but I have not found it explicitly defined anywhere. The bosonic worldvolume action reads [1] \begin{equation} S = \frac{\mu_5}{g_s}...
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25 views

Proper fully defined notation for angular velocity

Yeah, so, I know that objects rotate, about a point, in a chosen frame of reference. I was wondering if there is a mathematical notation that tells you the following : Point of rotation of a body ...
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1answer
58 views

Finding out the electric field intensity of an equilateral triangle [closed]

As I was practising some questions on electrostatics, I encountered a halt. I found this questions and was not able to solve it. Here is the question at hand, What does the point $d$ mean? I do not ...
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A question on Dirac delta function

If $$\int f(x)\frac{\mathrm{d}}{\mathrm{d}x}\delta(x-x’)\mathrm{d}x=-f’(x’)$$ What happens when I switch the integration and differentiation to $x’$ instead of $x$? Will I just get the negated result ...
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36 views

$SU(2)$ infinitesimal transformation of pion triplet lagrangian raising and lowering indices

How can I show that $$\epsilon^{ijk} (\partial^\mu\pi^i)\pi^j\partial_\mu\alpha^k(x)=\epsilon^{ijk}(\partial_\mu\pi^i)\pi^j\partial^\mu\alpha^k(x)~?$$ can I do the following? $\pi$ is the pion triplet ...
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Splitting beam of particles and its notation

Suppose we have a beam of particle $A_1$ which is split into beams $B_1$ ,$B_2$ and finally recombined into a final beam $A_2$. Suppose individually the beam states are denoted by $\psi_{A_1},\psi_{...
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36 views

What does the variable $n$ mean in the frequency of oscillation of drops?

I am currently working on a project to find how the frequency of oscillation of a water droplet falling through air depends on its surface tension and radius. I came across Lord Rayleigh's formulas: $...
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1answer
42 views

Analogous notation to $\nabla$ but for gradient with respect to $\vec{k}$ not $\vec{x}$

$\nabla = \frac{\partial}{\partial x_i}$ so $\nabla F = (\frac{\partial F}{\partial x}, \frac{\partial F}{\partial y}, \frac{\partial F}{\partial z})$. However, is there a similar equalivalent notion ...
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40 views

What $r_0 $ in the nucleus radius equation?

I'm doing some self-study and I'm attempting to calculate the energies needed to overcome the Coulomb barrier. I stumbled upon $R = r_0A^{1/3}$ for the radius of nuclei. I've been looking around ...
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57 views

What does the notation $^1 S_0$ represent in particle physics?

I'm coming across the notation $^1 S_0$, $^3 P_1$, $^1D_2$ etc. in relation to particle states. What do the two numbers and the letter represent? I've tried googling to no avail and it just appears in ...
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Partial derivative notation in thermodynamics

Most thermodynamics textbooks introduce a notation for partial derivatives that seems redundant to students who have already studied multivariable calculus. Moreover, the authors do not dwell on the ...
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181 views

Is the equation $[\nabla_{\mu},\nabla_{\nu}]=F_{\mu\nu}$ correct? If yes, how does it have to be interpreted?

It seems like simply using the equation \begin{equation} \nabla_{\mu}=\partial_{\mu}+A_{\mu} \end{equation} isn't enough: One obtains \begin{equation} [\nabla_{\mu},\nabla_{\nu}]=\underbrace{[\...
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1answer
81 views

Calculating Jacobian of transformation

In Sean Carroll's GR book, pg. 89, there is this equation (2.93) involving the Jacobian of a general transformation: $$\frac{\partial x^{\mu_1}}{\partial x^{\mu_1'}}...\frac{\partial x^{\mu_n}}{\...
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85 views

Vector calculus in Electromagnetism [closed]

I found a problem which had $$\partial_i (A_j \vec{G})= (\vec{\nabla} .\vec{ A} )\vec{G}+ (\vec{A}.\nabla) \vec{G} $$ but my problem is what does $$\partial_i (A_j \vec{B})$$ even mean? it doesn't ...
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1answer
53 views

Dirac Equation and Notation

I need to ask something regarding the Dirac equation (for a charged particle in an electromagnetic field) with the slash notation, which i fail to understand. We have the Dirac equation with the slash ...
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2answers
32 views

Modified Spectroscopic Notation (Shankar)

In Shankar's Chapter on addition of angular momentum in his Principles of Quantum Mechanics (Chapter 15 of the 2nd edition), he includes the section attached after describing the basic strategy for ...
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1answer
76 views

What is the proper transcription of these Einsteinian equations?

I’m updating an ebook edition of a science fiction story by Fritz Leiber, Nice Girl with 5 Husbands. (Its copyright has expired.) The final paragraph of the story reads: In his casual reading he ran ...
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2answers
40 views

Conjugate momentum notation

I was reading Peter Mann's Lagrangian & Hamiltonian Dynamics, and I found this equation (page 115): $$p_i := \frac{\partial L}{\partial \dot{q}^i}$$ where L is the Lagrangian. I understand this is ...
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1answer
40 views

What does an “elementary value $\delta$ of a quantity” mean?

In page-11 of I.E irodov Fundamental laws of mechanics, some notation used in the book is introduced. There, it is said that $\delta$ denotes the elementary value of a quantity but what exactly does ...
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2answers
75 views

What does a.u. mean as unit (not astronomical unit) in graphs in physics publications?

For example, in this paper (also arXiv), it uses a.u. as the unit in multiple graphs for the quantiy $\frac{dI}{dV}$, for example in Figure 3. I am suspecting a.u. means "appropriate unit," ...
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1answer
76 views

Standard model notation on doublets

$\require{cancel}$ I have been introduced to electroweak theory in lectures and I wanted to check I understand the notation for the doublets, triplets etc. Take the first generation lepton left handed ...
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1answer
46 views

Indices Exchange

In General Relativity, we often face indices exchange; but I actually do not really understand how to change indices properly. For example: If I have $$ R_{ab}\partial_c \phi \partial^b\phi \delta g^{...
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1answer
101 views

Variation of a scalar field

I am varying a scalar field density with the term ${\cal L}~=~-\frac{1}{2}(\partial _\mu\phi)^2$ w.r.t the scalar field $\phi$. First of all i want to know if its true that: ${\cal L} = -\frac{1}{2}(\...
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Are there any units of measurement (other than the ohm) that are represented by non-latin characters? [closed]

We have the prefix μ and the unit Ω, but other than that we seem to not use any other greek letters (or any non-latin symbols for that matter) for specifying units. All other units – meters, seconds, ...
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5answers
131 views

Confusion about $\partial_\mu x^\mu = 4$

Why is it that $\partial_\mu x^\mu = 4$? I thought that $\partial_\mu x^\mu$ could be expanded as $$\partial_\mu x^\mu = -\partial_1x^1 + \partial_2x^2 + \partial_3x^3 + \partial_4x^4 \\ =-1+1+1+1\\ =...
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1answer
46 views

Basic question about commutation in Dirac notation

In a nutshell my question is: "In the bracket notation, we can operate in the bra and in the ket with the same operator like $$\langle a|(A|b\rangle)=(\langle a|A)|b\rangle~?$$ So this operations ...
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1answer
36 views

What does $AB$ mean in the paper On the Electrodynamics of Moving Bodies?

When reading through the paper "On the Electrodynamics of Moving Bodies" by Albert Einstein, my friends and I were confused by some of the notation used and how to interpret it. On page 3, ...
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1answer
38 views

Is there an accepted abbreviation for 'Abundance'?

I want to represent the product of the abundance of hydrogen and the mass of hydrogen. Same for helium, but I can't find an abbreviation. What notation would I use for:$$\frac{\rho_B}{Abundance_H\...
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1answer
81 views

Einstein summation convention when a sum of terms is present

I'm reading Landau / Liftshitz vol. 6 on fluid mechanics, and I encountered the expression (page 45, top): $$\frac{\partial v_i}{\partial x_k} + \frac{\partial v_k}{\partial x_i}.$$ The expression ...
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2answers
66 views

Is this sensible index placement for a Christoffel symbol of the second kind?

I am trying to wrap my head around index notation and I have found a question in a textbook I am unsure of the answer of. It gives the expression: $$ t_{jk} = Γ^{i}_{jk} u_{i} $$ and asks for an ...
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2answers
103 views

Matrix vs. bra ket notation (QM)

I have a question. It's very simple to understand, yet it doesn't make sense to me. Say we have a system with a 2D orthonormal basis $|1⟩$, $|2⟩$. For this system, the energy operator (Hamiltonian) is:...
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1answer
42 views

Meaning of notation: $\mathrm{Sm}\left(\mathrm{Fe}_{0.8} \mathrm{Co}_{0.2}\right)_{12}$

I am reading a research paper about magnetic materials based on $\mathrm{SmFe_{12}}$ compounds (https://doi.org/10.1016/j.actamat.2020.05.026). They talk about the material $\mathrm{Sm}\left(\mathrm{...
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83 views

The light of speed and 24 hours

The notions of meter and second had been created much earlier than the speed of light was calculated. The speed of light is $299792458 ~ \text{m/s}$, i.e. it is really close to $300 ~000$ km/s. Also, ...
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0answers
47 views

Commutation relation of four vectors [closed]

I was trying to prove that: $$[P_\mu, J_{\rho \sigma}] = i(\eta_{\mu \sigma} P_\rho - \eta_{\mu \rho} P_\sigma) $$ $\textbf{Attempt}$ $$\begin{align} [P_\mu, J_{\rho \sigma}] = [P_\mu, x_\rho P_\sigma ...
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1answer
102 views

Definition of the stress-energy tensor in terms of functional derivatives in G.R

I have found confusing definitions in various places regarding the stress-energy tensor, in particular when used to derive Einstein GR equations from the principle of stationary action. Some of these ...
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28 views

Correct expression for multipole expansion

Panofsky and Philips state the multipole expansion of a potential due to a volume charge distribution $\rho$ in a finite volume $V$ given by $\phi(\mathbf R)=\frac{1}{4\pi\epsilon_0}\int_V\frac{\rho(\...
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4answers
149 views

Newton's Law of Cooling: $\delta Q$ or $\mathrm{d}Q$?

In this popular answer, I invoked Newton's Law of Cooling/Heating: $$\dot{q}=hA\Delta T\tag{1}$$ $$\dot{q}=\frac{\mathrm{d} Q}{\mathrm{d}t}\tag{2}$$ $$\dot{q}=\frac{\delta Q}{\mathrm{d}t}\tag{3}$$ $$\...
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2answers
116 views

Are there differences in notation for the d'Alembert operator?

On Wikipedia the d'Alembert operator is defined as $$\square = \partial ^\alpha \partial_\alpha = \frac{1}{c^2} \frac{\partial^2}{\partial t^2}-\nabla^2 $$ However, my professor uses the notation: $$ \...
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48 views

Tensor Index notation vs Matrix notation Transpose

Referring to the answer in the following question: https://physics.stackexchange.com/a/349030/288587 I just cant figure out how to go from: $$ \eta_{\mu\nu} = \Lambda^\alpha_{\;\mu}\Lambda^\beta_{\;\...

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