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27

The thing is that $\mathrm{dm}$ is a single symbol, not a combination of two symbols. Yes, it can be understood in terms of a prefix and a base indicator, but it is still a single symbol. An analogy to the concatenation of variable is inappropriate. Reference to an authoritative statement: The grouping formed by a prefix symbol attached to a unit ...


26

Straight from the horse's mouth: Source: Bureau International des Poids et Mesures (Search for "dimensionless" for all guidelines.) The International Bureau of Weights and Measures (French: Bureau international des poids et mesures), is an international standards organisation, one of three such organisations established to maintain the ...


25

This is not really an answer to your question, essentially because there isn't (currently) a question in your post, but it is too long for a comment. Your statement that A co-ordinate transformation is linear map from a vector to itself with a change of basis. is muddled and ultimately incorrect. Take some vector space $V$ and two bases $\beta$ and ...


21

It is an ångström, a unit of length commonly used in chemistry to measure things like atomic radii and bond lengths. Although not an official SI unit, it has a simple relationship to the metric units of length: $$1\:\mathrm{ångström} = 1\:\mathrm{Å} = 10^{−10}\:\mathrm{m} = 0.1\:\mathrm{nm} = 100\:\mathrm{pm}.$$


19

The symbol $\Delta$ refers to a finite variation or change of a quantity – by finite, I mean one that is not infinitely small. The symbols $d,\delta$ refer to infinitesimal variations or numerators and denominators of derivatives. The difference between $d$ and $\delta$ is that $dX$ is only used if $X$ without the $d$ is an actual quantity that may be ...


16

The main distinction you want to make is between the Green function and the kernel. (I prefer the terminology "Green function" without the 's. Imagine a different name, say, Feynman. People would definitely say the Feynman function, not the Feynman's function. But I digress...) Start with a differential operator, call it $L$. E.g., in the case of ...


13

It is, in fact, a double integral! The first notation used $$\varPhi_E = \oint_S \vec{E} \cdot \mathrm{d}\vec{A} = \oint_S \vec{E} \cdot \hat{n} \ \mathrm{d}A$$ is simply a more compact notation. It's much easier to write $\mathrm{d} \vec{A}$ instead of, say, $r \ \mathrm{d}r \ \mathrm{d}\theta$ all the time. Furthermore, it's more general, as $\mathrm{d} ...


11

It means that only when m and n are equal the value is 1, otherwise it is zero. Check http://en.wikipedia.org/wiki/Kronecker_delta for more information.


11

I've seen "(1)" used. Radians (and steradians) are also "unitless" but they're clearly not appropriate here.


11

It's c for constant or celeritas, which means speed in Latin. Everyone uses it because it's convention. You could use $\xi$ or $\zeta$ or $\gamma$ or any other symbol you wanted, but then you'd have to explain what it meant, and people would have to go through the trouble to remember this every time they read your papers. Better to go with convention and ...


10

Quite often everything inside bra or ket is just a label. In this particular case the meaning of $|λ,m_l⟩$ is "a state with the square of the angular momentum being equal to $λ$ (in atomic units, where $\hbar=1$) and with the projection of the angular momentum in some direction ($z$-axis conventionally) being equal to $m_l$". That is, $|λ,m_l⟩$ state is ...


9

Here is a video of the film's science advisor explaining what the equation is and how he came up with it: http://www.youtube.com/watch?v=WjfT6MqTCqQ It is based on the Gompertz equation, which is a model of mortality rates, with some added "mathematical glitter."


9

They're not used because it's ugly to read such texts with parentheses and it's time-consuming to write it down. A decimeter is indeed a "product" of "deci" and a meter, so the origin is analogous to the product of two real numbers $ab$. But once we define the new derived unit ${\rm dm}$, we treat it as a single object, so it really means what you would ...


8

There is, I think, no really standard symbol for the generic (chiral) CFT used universally, but there is within the different formalizations. When chiral CFTs are modeled by vertex operator algebras, the standard symbol is usually "$V$" (for obvious reasons) as user388027 notes in his reply.. When chiral CFTs are modeled as conformal nets, then (as you ...


8

Ben-Zvi & Frenkel denote vertex algebras $V$,$W$,... They're using the labels specifically for the spaces of states, but one could also use them to refer the whole package. Alternately, one sometimes sees all caps abbreviations: $YM_2$, $SYM_{4,G}$,... There is not to my knowledge any conventional notation for morphisms of field theories.


8

You are correct. $\Psi^{*}$ denotes the complex conjugate.


8

Each of the indices in a tensor have a particular left-right ordering. This ordering cannot be changed unless the tensor has some particular symmetry that permits it (or rather, that equates different components on interchange). The up-down positions of indices tells us about whether the index is associated with using a basis vector (up) or a basis ...


8

Are those square brackets standard notation in Physics? Yes. See, for example Sean Carroll notes. At least I can tell you from two other classic references using that notation, "General Relativity" by Wald (1984) and "A First Introducion to General Relativity" by Schutz (2009 for the most recent edition) $ $ If I am in a non-curved $\mathbb M$ ...


8

The antisymmetric part is defined as $$ A_{[a_1 \cdots a_n]} = \frac{1}{n!} \sum\limits_{\sigma \in P(n)} \text{sgn}(\sigma)A_{a_{\sigma(1)} \cdots a_{\sigma(n)}} $$ where $P(n)$ is the set of all permutations of the set $\{1,\cdots,n\}$. $\text{sgn}(\sigma)$ is called the sign of the permutation and is positive of $\sigma$ is obtained from the identity ...


8

A physicist would write your first equation $x^a = x^\mu e_\mu^a$. The notation $x^a$ is invariant in your terminology. The $a$ is an abstract index. It is ostensibly not supposed to be thought of as ranging over a set of numerical values, but is just a marker that indicates that $x$ is a vector (i.e., rank 1,0 tensor.) Similarly for each $\mu$, $e^a_\mu$ is ...


7

My taste, never overload your notation unless its necessary. Many people in quantum information try to avoid "hats" or further ornaments for operators that are just linear maps. Simple capital letters are fine to write Hamiltonians, channels, unitaries and measurements (italics are not really important, but its a de-facto standard). When people write ...


7

It is just a matter of notations. For some reasons, physicists tends to note position using a function notation $\hat \psi(x)$, and momentum with a subscript $\hat a_k$. It is just a matter of taste $\hat \psi(x)=\hat \psi_x$. You seem to be confused by the use of a continuous value for the "index" $x$. If you prefer (and I think that is what mathematicians ...


7

It's an integral over a closed line (e.g. a circle), see line integral. In particular, it is used in complex analysis for contour integrals (i.e closed lines on a complex plane), see e.g. example pointed out by Lubos. Also, it is used in real space, e.g. in electromagnetism, in Faraday's law of induction (part of the Maxwell equations, written in an ...


7

There is no significance in the choice between upper- and lower-case $\psi$ (or $\Psi$) to denote a system's wavefunction. The two are used interchangeably and it is the author's discretion to use either symbol. (On the other hand, of course, one shouldn't use the two symbols interchangeably within the same text; if both are used they would refer to ...


6

For conformal nets $\mathcal A,\mathcal B,\ldots$ or $A,B,\ldots$ is typical. For Virasoro nets $\mathrm{Vir}_{c=\frac 12}$ is normally used and for loop group nets $\mathcal A_{G_k}$. In VOA it seems to be common to use $V$ for a generic VOA. Kac uses in "VOA for Beginners" $V_Q$ for the lattice VOA associated with a lattice $Q$ and $V^k(\mathfrak g)$ for ...


6

As you see, there are different notations for quantum mechanical. Typically, even within a journal there is no one typesetting (style guides usually don't touch this topic). Besides the ones you mentioned, sometimes people use: bold font (e.g. ${\mathbf H}$), small font for operators acting on subsystems. Try looking at common notations used by your ...


6

In component notation, 3d and 4d vectors are usually distinguished using latin and greek letters respecitively, e.g. $u_i$ and $u_\mu$. Moreover, four-vectors without indices are usually just written as $u$, whereas three-vectors are denoted $\vec u$, as you say. You'll hardly find $\vec u$ denoting a four-vector. The option $\underline{u}$ is also ...


6

The author uses this weird notation $[c:\gamma]$ to represent complex numbers. It means: c is short for the mag­ni­tude $|c|$ of c, $\gamma$ is the phase of c. I have never seen this before either ;-). The author explains it earlier in his book, check out this link.


6

The convention I have seen in journal articles, and that I prefer, is to simply omit any mention of units for dimensionless quantities. EDIT: I also see the style Emilio Pisanty recommends, particularly in tables and graphs. For a graph, the idea is that the datapoints you are plotting are actually numbers, so you want to divide them by the relevant base ...


6

An alternative is to use the (slightly) more formally correct convention Length/m and Force/N for the first two, in which case simply using Safety Factor will work.



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