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2
votes
1answer
115 views

A simple question about matrix product with spinor indices

I have a big problem with dotted and undotted spinor indices. For example, suppose we have two convolutions: $$ \sigma^{\dot {a} a}F_{ab}, \quad \sigma^{\dot {a} a}F_{\dot {a} \dot {b}}, \quad F_{ab} ...
2
votes
1answer
226 views

Atomic nearest neighbor notation

I recently got a correction to a paper that I am writing. The correction references a section in which I talk about nearest neighbors. The comment says: Do you mean NN, NNN, etc., or NN, 2NN, 3NN? ...
5
votes
1answer
220 views

Why the speed of light is represented by $c$? [closed]

In almost every textbook, I've found that the speed of light is $c \approx 3 \times 10^8\: \mathrm{m/s}$. I wonder why it's just $c$ ?
1
vote
0answers
47 views

Are derivative indices summed in indicial notation?

A paper I'm reading uses indicial notation and the convention that $u_{j,k}$ means the derivative with respect to $x_k$. Which one of these interpretations are correct? $$A_{ijk}u_{j,k} = ...
0
votes
0answers
72 views

How should the implicit sum $C_{ijkl}u_{i,j}u_{k,l}$ be interpreted?

$C$ is a 3x3x3x3 tensor. How should the expression $C_{ijkl}u_{i,j}u_{k,l}$ be interpreted? This is my guess: $$ \sum_{i=1}^3\sum_{j=1}^3 \sum_{k=1}^3\sum_{l=1}^3 C_{ijkl}u_{i,j}u_{k,l} $$
0
votes
2answers
82 views

What is this form of notation called?

$$^{14}_6C \rightarrow ^{14}_7N + E^{-} + \bar{\nu}_e$$ Just curious!
2
votes
2answers
139 views

Affine connection notation

Can ${g}^{\mu\sigma}{\Gamma}^{\rho}_{\sigma\nu}$ be written as ${\Gamma}^{\mu\rho}_{\nu}$? If so how come this symbol never appears in any GR book?
2
votes
2answers
425 views

Bracket Notation on Tensor Indices

I know about the () symmetrisation and [] anti-symmetrisation brackets on tensor indices so long as they appear on their own, such as : $$V_{[\alpha \beta ]}=\frac{1}{2}\left ( V_{\alpha \beta ...
1
vote
2answers
173 views

Dealing with dirac notation with regards to different basis'

So this should be a pretty simple question. So we say that $\langle x | \psi \rangle = \psi(x)$. In other words $\psi(x)$ is the ket $|\psi\rangle$ expressed in terms of the $x$ basis. Now suppose ...
7
votes
1answer
428 views

Ж (“zhe”) in string theory?

I was just recently watching a TED talk about string theory, by Thad Roberts, and at around 11:10 into the video he mentions a constant for maximum spacial curvature called "zhe" (the Cyrillic symbol ...
2
votes
0answers
235 views

Why the letter $B$ for magnetic fields? [closed]

Is there a reason behind the usage of this letter to represent magnetic fields, or is it a randomly made choice?
1
vote
1answer
122 views

What does $\nu$ mean in relativity?

I decided to teach myself relativity over the Christmas holiday, and I've gotten a bit stuck. Coordinates in space time can be defined by a collection of coordinates, $$ x^0 = ct \\ x^1 = x \\ x^2 = ...
6
votes
1answer
266 views

How are the definitions of a coherent state equivalent?

I am trying to understand coherent states. As far as I could find there are three equivalent definitions and in general many sources start from a different one, still I fail to see their equivalence. ...
7
votes
2answers
1k views

Derivative with respect to a vector is a gradient?

I've encountered in some books (and even completed an exercise from the Goldstein by using it), a strange notation that seems to work exactly like a gradient, I have tried to look for an explanation ...
4
votes
1answer
106 views

Higgs mechanism in QED

I'm trying to understand the Higgs mechanics. For that matter, I'm exploring the possibility of giving mass to the photon in a gauge-invariant way. So, if we introduce a complex scalar field: $$ ...
5
votes
3answers
303 views

Error in books of conformal field theory?

If you look at the book Conformal Field Theory (by Philippe Francesco, Pierre Mathieu and David Senechal) or the lecture notes Applied Conformal Field Theory (by Paul Ginsparg), and many other places: ...
1
vote
1answer
72 views

Gradient of a two-component field

I have a two-component field: $$\phi(\vec{x}) = \left( \begin{array}{c} \phi_1(\vec{x}) \\ \phi_2(\vec{x}) \end{array} \right)$$ with $\phi^T = (\phi_1, \phi_2)$. And I am trying to evaluate: ...
0
votes
1answer
215 views

Notation in Quantum Mechanics

When we write equations in QM, in certain places, the wave function is represented as $\psi(x,t)$, which is the wave function in position space, and in some other places, it is written as $\Psi(t)$. ...
2
votes
1answer
62 views

What is the chemical symbol for Mu-mesic atoms?

Is there a convention for chemical symbols of mu-mesic atoms, at least for ones bound to light atomic nuclei?
1
vote
1answer
202 views

Understanding vectors in physics: notation

We have the formula for the Lorentz force $$\textbf{F} = q \space(\textbf{E} + \textbf{v} \times \textbf {B})$$ This is a simple formula you learn in high school, but I'm interested to self-study ...
3
votes
1answer
196 views

What does $|x⟩|0⟩$ actually mean in bra-ket notation?

Consider the following quote from Wikipedia's page on Shor's algorithm: Initialize the registers to $Q^{-1/2} \sum_{x=0}^{Q-1} \left|x\right\rangle \left|0\right\rangle$ where $x$ runs ...
3
votes
1answer
110 views

What do physicists mean by ${g^{i}}_j$?

Maybe this is an idiot question, but in relativity I see a lot of ${g^{i}}_j$ for a metric tensor $g$. Is this just $$\delta^i_j ~=~ g(dx^i \sharp, \partial_{ x^j})~?$$
7
votes
2answers
267 views

Historical reason behind using $ν$ instead of $f$ to stand for frequency in the equation $E=hν$?

Normally, we use the letter $f$ to stand for frequency in equations. $$T = 1/f$$ $$v = \lambda f$$ $$Φ +E_k = h f$$ So I'm curious as why the letter $ν$ (nu) is used to represent frequency in the ...
1
vote
1answer
97 views

Notation: What is $\delta_{mn}$?

In a textbook, I found this relation for eigenvalues of total angular momentum: $$(L^2)_{mn} = \langle l,m \rvert L^2 \lvert l,n\rangle = \hbar^2l(l+1)\delta_{mn}$$ What is the $\delta_{mn}$ refer ...
10
votes
5answers
1k views

What exactly is $\hat{\psi}^\dagger(x)$? An operator or a function?

I've recently read Cohen-Tannoudji on quantum mechanics to try to better understand Dirac notation. A homework problem is giving me some trouble though. I'm unsure if I've learned enough yet to ...
3
votes
1answer
203 views

Notations for statistical / systematic / numeric errors?

I constantly see the notation $$ 5.143(13) $$ for specifying that a value was measures / calculated to be 5.143 with an estimated error of 0.013. I have come to wonder though, just how commonly ...
2
votes
2answers
560 views

Notation for anti-symmetric part of a tensor

I know that $A_{[a} B_{b]} = \frac{1}{2!}(A_{a}B_{b} - A_{b}B_{a})$ But how can write $E_{[a} F_{bc]}$ like the above? Can you provide a reference where this notational matter is discussed?
3
votes
2answers
160 views

How to deal with the notation of a function $f$ vs its value $f(x)$ in Physics?

This doubt is very silly, but anyway, I think it's worth asking. The problem is: when we work with mathematics, in many situations we want to consider sets $A$ and $B$ and functions $f : A \to B$. ...
0
votes
2answers
494 views

Feynman's subscript notation

Consider this vector calculus identity: $$ \mathbf{A} \times \left( \nabla \times \mathbf{B} \right) = \nabla_\mathbf{B} \left( \mathbf{A \cdot B} \right) - \left( \mathbf{A} \cdot \nabla \right) ...
3
votes
3answers
257 views

Question about the Dirac notation for partial trace

I saw the following definition for the partial trace operator: $\rho_A=\sum_k \langle e_k|\rho_{AB}|e_k\rangle$, where $e_k$ is basis for the state space of system $B$. From what I know, in the ...
2
votes
1answer
221 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
488 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
140 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
350 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
279 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
82 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
634 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 ...
0
votes
3answers
2k 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
290 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
200 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
290 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
165 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
302 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
495 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
1k 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
288 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 ...
15
votes
2answers
5k 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
410 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
295 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
196 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 ...