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2
votes
1answer
172 views

Term symbol - how do we know the number of electrons $e^-$?

Lets say I have a term symbol $^4D_{5/2}$. From this I can simply read the total quantum numbers numbers $L=2$ and $J=5/2$. Now the superscripted number $4$ is called multiplicity if I am not ...
1
vote
2answers
323 views

How do you show from the index notation that the change of frame formula for a metric must involve the transpose?

Let $x^\mu$ and $x^{'\mu}$ be two coordinate systems related by $$dx^{'\mu}~=~S^\mu{}_\nu~ dx^\mu.$$ In index notation the metric in both systems are related by: ...
2
votes
0answers
113 views

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 ...
1
vote
2answers
267 views

Should we necessarily express the dimensions of a physical quantity within square brackets? [duplicate]

For example, should we write the dimension of mass, e.g. $\mathrm{kg}$ as $[M]$ or is it enough to write it as $M$?
1
vote
0answers
211 views

Field Strength Renormalisation in Peskin and Schroeder

In chapter 7 of Peskin and Schroeder they define the field strength renormalisation $Z$ for a quantum field to be the residue of the Fourier transform of the correlation function $$\langle \Omega | ...
0
votes
1answer
74 views

Possible abuse of notation in statistical mechanics

I know that it often occurs that we need to take a derivitive with respect to $\beta$ in statistical mechanics. However, I think it is poor style to use equations with both T and $\beta$ in them ...
0
votes
2answers
538 views

Basic question on bra-ket notation

Which of the following corresponds to a $ \psi(x)$, a wavefunction written in the position basis: $ x| \psi\rangle $ or $ \langle x| \psi\rangle $? If it is the second expression (which my textbook ...
-1
votes
3answers
1k views

What is Si-delta doping? [closed]

I want to know what the delta means in this case. I know the Si means the element used, by some way to doping. I guess the delta means that using some elements to create holes in semiconductor made ...
1
vote
1answer
183 views

spin parity $J^P$ notation

In particle physics, when you read $J^P$, does it mean Spin parity or total angular momentum parity? I know that the letter $J$ is used for TOTAL angular momentum but I think I read somewhere that ...
0
votes
1answer
172 views

Einstein Notation for Strain Energy Function

I encounter the following formula (for strain energy function) a lot in physics literature: $$ W(\epsilon_{kl}) = \int_0^{\epsilon_{kl}} \sigma_{ij} \textrm{d}\epsilon_{ij} $$ where all indices ...
3
votes
1answer
238 views

Notation for Standard Model Charges?

Does anybody know what these following numbers describing an electron $(1, 1, -1)$ represent in $SU(3) \times SU(2) \times U(1)$? Or, these numbers that describe an up quark: $(3, 1, 2/3)$? I'm ...
3
votes
0answers
149 views

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 ...
2
votes
3answers
244 views

On Einstein notation with multiple indices

On Einstein notation with multiple indices: For example, consider the expression: $$a^{ij} b_{ij}.$$ Does the notation signify, $$a^{00} b_{00} + a^{01} b_{01} + a^{02} b_{02} + ... $$ i.e. you ...
4
votes
2answers
398 views

What is the gamma five matrix $\gamma_5$?

This Wikipedia page explains that for each of the four main gamma matrices $\gamma^{\mu}$, you can find the covariant matrices $\gamma_{\mu}$ with the equation $\gamma_{\mu} = ...
1
vote
2answers
703 views

Kronecker delta confusion

I'm confused about the Kronecker delta. In the context of four-dimensional spacetime, multiplying the metric tensor by its inverse, I've seen (where the upstairs and downstairs indices are the same): ...
5
votes
2answers
247 views

In what order should unit symbols appear?

I am trying to represent the result of a dimensional analysis calculation and I can't find an official document that lists the order that unit symbols should appear. For example, when I google ...
12
votes
2answers
3k views

Difference between $\Delta$, $d$ and $\delta$

I have read the thread regarding 'the difference between the operators between $\delta$ and $d$', but it does not answer my question. I am confused about the notation for change in Physics. In ...
0
votes
1answer
316 views

Some Dirac notation unclarities

Q1: Ok so i have come to a point where i know that $\Psi(r,t)$ which we denote only by $\Psi$ can be represented in a Hilbert space by a vector which we denote $\left|\Psi\right\rangle$. Does this ...
6
votes
2answers
239 views

Why distinguish between row and column vectors?

Mathematically, a vector is an element of a vector space. Sometimes, it's just an n-tuple $(a,b,c)$. In physics, one often demands that the tuple has certain transformation properties to be called a ...
2
votes
2answers
155 views

Vector $\vec{z}$ and its conjugate transpose $\overline{\vec{v}^\top}$ - is it the same as $\left|z\right\rangle$ and $\left\langle z \right|$

Lets say we have a complex vector $\vec{z} \!=\!(1\!+\!2i~~2\!+\!3i~~3\!+\!4i)^T$. Its scalar product $\vec{z}^T\!\! \cdot \vec{z}$ with itself will be a complex number, but if we conjugate the ...
2
votes
1answer
76 views

Scalar top quark (stop) pair production

A rather simple question: Starting from an electrically neutral state, pairs of top quarks are produced as top and anti-top, and denoted as $t\bar t$. Now the production of pairs of scalar top ...
4
votes
2answers
208 views

Difference between slanted indices on a tensor

In my class, there is no distinction made between, $$ C_{ab}{}^{b} $$ and $$ C^{b}{}_{ab}. $$ All I know, and read about so far, is the distinction of covariant and contravariant, form/vector, etc. ...
17
votes
8answers
3k views

Is there a symbol for “unitless”?

I'm making a table where columns are labelled with the property and the units it's measured in: Length (m) |||| Force (N) |||| Safety Factor (unitless) ||| etc... I'd like not to write "unitless" ...
3
votes
2answers
215 views

Inner Product Spaces

I am trying to reconcile the definition of Inner Product Spaces that I encountered in Mathematics with the one I recently came across in Physics. In particular, if $(,)$ denotes an inner product in ...
-1
votes
1answer
171 views

Vector Addition — Direction

Say we have three forces $F_1, F_2, F_3$, such that $$ F_1 + F_2 - F_3 = 0\hspace 10mm (1) $$ And let us say that $F_1$ and $F_2$ have the same direction and magnitude, and that $F_3$ has double the ...
0
votes
2answers
126 views

A tensor summation question

With the definition of the tensor: \begin{equation} J_{ij} = I_{ij} - \tfrac{1}{3}\delta_{ij}I^{k}_{k}, \qquad i,j,k\in\{1,2,3\}, \end{equation} I have seen the quantity: \begin{equation} ...
2
votes
1answer
187 views

What does the notation $c = [1:\beta]$ mean?

I have been reading a online-book/blog/material on Quantum Mechanics, when I encountered a notation on a page and I have no idea what it means. See if you can help. Here's the link and follows the ...
5
votes
0answers
114 views

Is it correct to sum over either index of the metric the same way?

I don't know if the following is correct, i want to compute the following derivative $$\frac{\partial }{\partial (\partial_{\mu}A_{\nu})}\left(\partial^{\alpha}A^{\beta}\partial_{\alpha}A_{\beta} ...
2
votes
1answer
135 views

Reaction coordinate as a function of atomic positions

I'm going over some (molecular dynamics) related literature - specifically the derivation of the Weighted Histogram Analysis Method (WHAM). As a quick backdrop WHAM is a method for stitching ...
4
votes
2answers
2k views

Derivatives of operators

How do derivatives of operators work? Do they act on the terms in the derivative or do they just get "added to the tail"? Is there a conceptual way to understand this? For example: say you had the ...
-1
votes
1answer
580 views

Differences between orthogonality and Kronecker delta function? [closed]

If $i$ and $j$ are two variables then Kronecker delta is written as $$\delta_{i,j}~:=~\begin{cases}1 \hspace{3mm} \mbox{if} \hspace{3mm} i=j,\\ 0 \hspace{3mm}\mbox{if} \hspace{3mm}i \neq ...
1
vote
1answer
1k views

Wave function and Dirac bra-ket notation

Would anyone be able to explain the difference, technically, between wave function notation for quantum systems e.g. $\psi=\psi(x)$ and Dirac bra-ket vector notation? How do you get from one to the ...
2
votes
2answers
132 views

Double Pendulum

The equations of motions for the double pendulum is given by $$\dot{\theta_1} = \frac{6}{ml^2}\frac{2p_{\theta1} - 3\cos(\theta_1 - \theta_2)p_{\theta2}}{16 - 9\cos^2(\theta_1 - \theta_2)}$$ and ...
0
votes
2answers
1k views

Proper notation for normalized scalar?

I have not been able to find a resource to tell me the standard notation for a normalized scalar value. Normalized vectors (i.e. unit vectors) are typically denoted by placing a hat over the ...
2
votes
2answers
400 views

In Dirac notation, what do the subscripts represent? (Solution for particle in a box in mind)

So the set of solutions for the particle in a box is given by $$\psi_n(x) = \sqrt{\frac{2}{L}}\sin(\frac{n\pi x}{L}).$$ In Dirac notation $<\psi_i|\psi_j>=\delta_{ij}$ assuming $|\psi_i>$ ...
1
vote
2answers
188 views

From differentials to differential equations

Suppose I have a function of time $t$ and position $(x,y)$ such that \begin{equation} p_t \,dt = p \,dy - p_x (1-x) \,dx + p_y \,dy\end{equation} where the subscript denotes a differentiation. In this ...
2
votes
2answers
6k views

What does y with a line over it represent?

I've been asked to complete this chart and have never come across this symbol before, nor can I find anything about it on google: What does the y with the line over it represent? And also, does the ...
2
votes
1answer
606 views

Difference between $\partial$ and $\nabla$ in general relativity

I read a lot in Road to Reality, so I think I might use some general relativity terms where I should only special ones. In our lectures we just had $\partial_\mu$ which would have the plain partial ...
4
votes
1answer
331 views

Clarifications about Poisson brackets and Levi-Civita symbol

I need some clarifications about Poisson brackets. I know canonical brackets and the properties of Poisson Brackets and I also know something about Levi-Civita symbol (definition and basic ...
0
votes
2answers
183 views

Meaning of juxtaposition of vectors

I came across some notation that I can't quite understand: $$ \hat{r}\hat{r} - \textbf{1}_3$$ where $\textbf{1}_3$ is the 3$\times$3 identity matrix, $\hat{r}$ is a unit 1$\times$3 vector, and the ...
1
vote
2answers
179 views

Notation for differential operators and wave function math

I know that $[\frac {d^2}{dx^2}]\psi$ is $\frac {d^2\psi}{dx^2}$ but what about this one $[\frac {d^2\psi}{dx^2}]\psi^*$? Is it this like $\frac {d^2\psi\psi^*}{dx^2}$ or this like $\frac ...
3
votes
6answers
1k views

Is H=H* sloppy notation or really just incorrect, for Hermitian operators?

I saw it in this pdf, where they state that $P=P^\dagger$ and thus $P$ is hermitian. I find this notation confusing, because an operator A is Hermitian if $\langle \Psi | A \Psi \rangle=\langle A ...
1
vote
4answers
297 views

Is there a default notation for 4-vectors while handwriting?

In printed paper 3-vectors can be denoted bold italic while 4-vectors can be denote just bold. While handwriting 3-vectors are denoted by arrows above letters. Is there a similar way to denote ...
2
votes
1answer
68 views

Uncertainty writing

This will sound like a silly question, but I don't recall that my professors ever though me what this means. For example: X=1.2345(6) units This is uncertainty, that much I do know, but does it ...
2
votes
2answers
163 views

SI units with more than one prefix in fractions

Is it (in the view of SI) correct to note units with more then one prefix? I discuss this since several months with friends, but we could not find a proper source for our statements yet. Examples for ...
0
votes
1answer
2k views

Mutual Inductance and the Dot Convention

Can anyone please explain me, the dot convention in coil systems (Mutual and self inductance) with some related images to understand..?
3
votes
2answers
283 views

What are $\partial_t$ and $\partial^\mu$?

I'm reading the Wikipedia page for the Dirac equation: $\rho=\phi^*\phi\,$ ...... $J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$ with the conservation of probability ...
0
votes
1answer
191 views

Notation for two variables with same dimensions [duplicate]

What symbol represents "has the dimensions of", as in "x has the dimensions of d"? Does such a symbol exist?
6
votes
2answers
421 views

What the circled integral?

What the circled integral $$ \oint $$ means? I saw this symbol in a lot of books about advanced physics. How is his definition? What kind of integral it is? It is used only in physics or also in ...
2
votes
2answers
380 views

Meaning of subscript in $V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$

This is probably a simple question, but what does the subscript $0$ mean in the following expression? $$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$