The notation tag has no wiki summary.
17
votes
8answers
1k 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" ...
15
votes
1answer
1k views
Differentiating Propagator, Greens function, Correlation function, etc
For the following quantities respectively, could someone write down the common definitions, their meaning, the field of study in which one would typically find these under their actual name, and most ...
13
votes
4answers
2k views
What does Peter Parkers formula represent?
Okay, so the trailer for the new Spider Man movie is out and appearently our friendly physicist from the neightborhood came up with something. However I can't find out what this is.
...
9
votes
2answers
488 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 ...
6
votes
2answers
305 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 ...
5
votes
3answers
63 views
which letter to use for a CFT?
In math, one says "let $G$ be a group", "let $A$ be an algebra", ...
For groups, the typical letters are $G$, $H$, $K$, ...
For algebras, the typical letters are $A$, $B$, ...
I want to say ...
5
votes
2answers
170 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 ...
5
votes
4answers
297 views
Are covariant vectors representable as row vectors and contravariant as column vectors
I would like to know what are the range of validity of the following statement:
Covariant vectors are representable as row vectors. Contravariant
vectors are representable as column vectors.
...
4
votes
2answers
116 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. ...
4
votes
2answers
184 views
Standard notation reference
I'm searching for a compresensive and somewhat complete list of suggested standard notation (the symbols one ought to use in (theoretical) physics and also mathematics).
Is there such a collection, ...
4
votes
2answers
80 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} = ...
4
votes
1answer
276 views
Why is $L^2$ norm of the gradient called kinetic energy?
I'm reading Lieb-Loss's book 'Analysis', chapter 7. The authors refer to the following integral:
$$\tag{1} \lVert \nabla f\rVert_2^2=\int_{\Omega}\lvert \nabla f(x)\rvert^2\, d^nx $$
as the kinetic ...
4
votes
2answers
83 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 ...
4
votes
1answer
168 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 ...
4
votes
1answer
76 views
$\pm$ (light-cone?) notation in supersymmetry
I would like to know what is exactly meant when one writes $\theta^{\pm}, \bar{\theta}^\pm, Q_{\pm},\bar{Q}_{\pm},D_{\pm},\bar{D}_{\pm}$.
{..I typically encounter this notation in literature on ...
4
votes
0answers
95 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} ...
3
votes
6answers
429 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 ...
3
votes
4answers
127 views
Is there a recognised standard for typesetting quantum mechanical operators?
Firstly, I wasn't sure exactly where to put this. It's a typesetting query but the scope is greater than $\TeX$; however it's specific also to physics and even more specific to this site.
I've ...
3
votes
2answers
376 views
Bra-ket notation and linear operators
Let $H$ be a hilbert space and let $\hat{A}$ be a linear operator on $H$.
My textbook states that $|\hat{A} \psi\rangle = \hat{A} |\psi\rangle$. My understanding of bra-kets is that $|\psi\rangle$ is ...
3
votes
2answers
197 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 ...
2
votes
3answers
240 views
How to distinguish 4D and 3D vectors in handwriting?
Usually vectors are denoted with bold font in printbooks and with arrows above in handwriting.
In Thorn's e al. Gravitation, 4D vectors are denoted with bold and 3D vectors with bold italic. How to ...
2
votes
1answer
193 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 ...
2
votes
1answer
110 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 ...
2
votes
2answers
85 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)}$$
and ...
2
votes
1answer
187 views
Meaning of $d\Omega$ in basic scattering theory?
In basic scattering theory, $d\Omega$ is supposed to be an element of solid angle in the direction $\Omega$. Therefore, I assume that $\Omega$ is an angle, but what is this angle measured with respect ...
2
votes
3answers
107 views
On Einstein notation with multiple indices
On Einstein notation with multiple indices: For example, consider the expression:
$$a^{ij} b_{ij}.$$
Does the notation signify,
$$a^{00} b_{00} + a^{01} b_{01} + a^{02} b_{02} + ... $$
i.e. you ...
2
votes
1answer
51 views
Scalar top quark (stop) pair production
A rather simple question:
Starting from an electrically neutral state, pairs of top quarks are produced as top and anti-top, and denoted as $t\bar t$.
Now the production of pairs of scalar top ...
2
votes
2answers
146 views
Inner Product Spaces
I am trying to reconcile the definition of Inner Product Spaces that I encountered in Mathematics with the one I recently came across in Physics. In particular, if $(,)$ denotes an inner product in ...
2
votes
1answer
60 views
Uncertainty writing
This will sound like a silly question, but I don't recall that my professors ever though me what this means. For example:
X=1.2345(6) units
This is uncertainty, that much I do know, but does it ...
2
votes
2answers
256 views
Meaning of subscript in $V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$
This is probably a simple question, but what does the subscript $0$ mean in the following expression?
$$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$
2
votes
2answers
309 views
Correct application of Laplacian Operator
Not a physicist, and I'm having trouble understanding how to apply the Laplacian-like operator described in this paper and the original. We let:
$$ \hat{f}(x) = f(x) + \frac{\int H(x,y)\psi(y) ...
2
votes
2answers
62 views
Another question about Shankar's notation
I have another question on the notation in Shankar. I think it's sloppy, but I also may just be misunderstanding it. Again, this is at the very beginning of the math intro.
He has:
$$a\left| V ...
2
votes
2answers
165 views
In Dirac notation, what do the subscripts represent? (Solution for particle in a box in mind)
So the set of solutions for the particle in a box is given by
$$\psi_n(x) = \sqrt{\frac{2}{L}}\sin(\frac{n\pi x}{L}).$$
In Dirac notation $<\psi_i|\psi_j>=\delta_{ij}$ assuming $|\psi_i>$ ...
2
votes
2answers
101 views
SI units with more than one prefix in fractions
Is it (in the view of SI) correct to note units with more then one prefix? I discuss this since several months with friends, but we could not find a proper source for our statements yet.
Examples for ...
2
votes
0answers
53 views
Group theory notation used in physics (AdS/CFT)
This in the context of the AdS/CFT correspondence. I am reading this review on AdS/CFT Aharony et. al. The abstract can be found here
Equation (2.50) of the above paper lists the $R$-symmetry groups ...
1
vote
2answers
250 views
Question with Einstein notation
Let’s consider this equation for a scalar quantity $f$ as a function of a 3D vector $a$ as:
$$ f(\vec a) = S_{ijkk} a_i a_j $$
where $S$ is a tensor of rank 4. Now, I’m not sure what to make of the ...
1
vote
4answers
183 views
Is there a default notation for 4-vectors while handwriting?
In printed paper 3-vectors can be denoted bold italic while 4-vectors can be denote just bold.
While handwriting 3-vectors are denoted by arrows above letters.
Is there a similar way to denote ...
1
vote
1answer
155 views
Rocket drive and conservation of momentum
I am currently reading through some lecture notes of Physics 1 and in a chapter about the dynamics of the mass point, there is an example covering the rocket drive.
Let $v$ be the velocity of the ...
1
vote
2answers
209 views
Question on notation in Shankar's Quantum Mechanics - math intro on vector spaces
I'm just beginning Shankar's 2nd edition Quantum Mechanics and having some trouble with notation. He defines his vectors as "$\left|V\right>$" . And with a scalar multiplier as "$a\left|V\right>$" . ...
1
vote
2answers
160 views
Why no basis vector in Newtonian gravitational vector field?
In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$
which is a vector field. On the same page, it is also given as a ...
1
vote
1answer
739 views
What does $\Psi^*$ mean in Schrodinger's Equation?
I am not a physics student. In one of my courses, some fundamental concepts of Quantum mech were needed, so i was gng through them when i stumbled upon this
It says
$$\text{probability} = ...
1
vote
2answers
55 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):
...
1
vote
2answers
227 views
Notation of plane waves
Consider a monochromatic plane wave (I am using bold to represent vectors)
$$ \mathbf{E}(\mathbf{r},t) = \mathbf{E}_0(\mathbf{r})e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t)}, $$
$$ ...
1
vote
1answer
59 views
What is $k_B$ in the context of this question?
Answering the following question
1000 atoms are in equilibrium at temperature T. Each atom has two
energy states, $E_1$ and $E_2$, where $E_2 > E_1$ . On average, there are 200
atoms in the ...
1
vote
1answer
284 views
state vector notation
I've never taken a quantum mechanics class, but I find myself now using principles developed in the quantum theory of angular momentum. One particularly confusing aspect that I'm struggling with is ...
1
vote
2answers
53 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 ...
1
vote
1answer
293 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 ...
1
vote
1answer
580 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:
http://postimage.org/image/oe7hb9cy3/
What does the y with the line ...
1
vote
2answers
128 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 ...
1
vote
1answer
166 views
Symbol for dashpot/damper (in a harmonic oscillator)
In diagrams that contain the dashpot symbol, sometimes the mass is attached to the "interior" end of the dashpot, other times the mass is attached to the "base" end.
For example, consider the ...
