Questions tagged [notation]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
36
votes
2answers
40k views

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

I have read the thread regarding 'the difference between the operators $\delta$ and $d$', but it does not answer my question. I am confused about the notation for change in Physics. In Mathematics, $\...
28
votes
2answers
2k views

Symbols of derivatives

What is the exact use of the symbols $\partial$, $\delta$ and $\mathrm{d}$ in derivatives in physics? How are they different and when are they used? It would be nice to get that settled once and for ...
47
votes
3answers
10k views

Mathematically-oriented Treatment of General Relativity

Can someone suggest a textbook that treats general relativity from a rigorous mathematical perspective? Ideally, such a book would Prove all theorems used. Use modern "mathematical notation" as ...
37
votes
8answers
5k views

Is it foolish to distinguish between covariant and contravariant vectors?

A vector space is a set whose elements satisfy certain axioms. Now there are physical entities that satisfy these properties, which may not be arrows. A co-ordinate transformation is linear map from a ...
13
votes
2answers
9k views

Do derivatives of operators act on the operator itself or are they “added to the tail” 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 ...
9
votes
3answers
1k views

Staggered Indices ($\Lambda^\mu{}_\nu$ vs. $\Lambda_\mu{}^\nu$) on Lorentz Transformations

I have some open-ended questions on the use of staggered indices in writing Lorentz transformations and their inverses and transposes. What are the respective meanings of $\Lambda^\mu{}_\nu$ as ...
2
votes
2answers
390 views

Understanding Dirac's notation

Let's say I have eigenstates $|x\rangle$ associated with measurement of position. I know that the eigenstates corresponding to their respective eigenvalues form a basis, let's call it $A$. Now let's ...
32
votes
2answers
19k views

Square bracket notation for dimensions and units: usage and conventions

One of the most useful tools in dimensional analysis is the use of square brackets around some physical quantity $q$ to denote its dimension as $$[q].$$ However, the precise meaning of this symbol ...
14
votes
4answers
9k views

Difficulties with bra-ket notation

I have started to study quantum mechanics. I know linear algebra,functional analysis, calculus, and so on, but at this moment I have a problem in Dirac bra-ket formalism. Namely, I have problem with "...
3
votes
3answers
2k views

Square bracket 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?
1
vote
3answers
891 views

Convention of tensor indices

Let $g_{ij}$ be the diagonal Minkowski metric tensor diag$(g) = (1,-1,-1,-1)$, then $g^{ij}$ is defined to be $(g^{-1})^{ij}$, hence $$g_{ik}g^{kj} = g_i^{\ \ j} = \text{diag}(1,1,1,1)=\delta_i^{\ \ j}...
9
votes
1answer
310 views

What do term symbols with a half-integer “$L$” like $^3[3/2]_{1/2}$ mean?

Atomic term symbols are used to notate the angular momentum content of the electronic states of an atom, and are normally written down as $$^{2S+1}L_J$$ where the state has total spin $S$, spin ...
6
votes
5answers
3k views

What is the meaning of following expression $C=\frac{\delta Q}{dT}$ mathematically?

Our professor raised the following question during our lecture in Statistical Physics (even so it's related to Thermodynamics): Many text books (even Wikipedia) writes wrong expressions (from ...
14
votes
2answers
12k views

Uncertainty in parenthesis

In a physics text book I read the following: $$e/m=1.758820150(44) ×10^{11} \mathrm{C/kg} $$ In this expression, $(44)$ indicates the likely uncertainty in the last two digits, $50$. How should ...
11
votes
1answer
838 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. ...
6
votes
1answer
2k views

Existence of adjoint of an antilinear operator, time reversal

The time reversal operator $T$ is an antiunitary operator, and I saw $T^\dagger$ in many places (for example when some guy is doing a "time reversal" $THT^\dagger$), but I wonder if there is a well-...
3
votes
1answer
6k 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 ...
32
votes
8answers
23k 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" ...
4
votes
1answer
503 views

Working with indices of tensors in special relativity

I'm trying to understand tensor notation and working with indices in special relativity. I use a book for this purpose in which $\eta_{\mu\nu}=\eta^{\mu\nu}$ is used for the metric tensor and a vector ...
3
votes
3answers
736 views

Is the shorthand $ \partial_{\mu} $ strictly a partial derivative in field theory?

The Euler-Lagrange equation for particles is given by $$ \frac{d}{dt}\frac{\partial L}{\partial \dot{q}} = \frac{\partial L}{\partial q},\tag{1}$$ and for fields it is $$ \partial_{\mu} \frac{\...
16
votes
4answers
4k views

Why is the candela a base unit of the SI?

The candela is defined as The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency $540\cdot10^{12}$ hertz and that has a radiant ...
6
votes
3answers
1k views

What is the meaning of the double complex integral notation used in physics?

In Altland and Simons' condensed matter book, complex Gaussian integrals are introduced. Defining $z = x + i y$ and $\bar{z} = x - i y$, the complex integral over $z$ is $$\int d(\bar{z}, z) = \int_{-\...
4
votes
2answers
703 views

Variation of Lagrangian density $\mathcal{L}$ w.r.t $x^{\mu}$

If a function $f(x(t),y(t))$ has no explicit dependence on the variable $t$, then $\frac{\partial f}{\partial t}=0$. In quantum field theory, the Lagrangian density $\mathcal{L}(\phi,\partial_\mu\phi)...
11
votes
3answers
1k views

Why is the $dx$ right next to the integral sign in QFT literature?

I've noticed that in QFT literature, integrals are usually written as $\int \!dx ~f(x)$ instead of $\int f(x) dx$. Why?
4
votes
3answers
313 views

In what subfields and how far can the naive limit $c\rightarrow\infty$ of special relativity be carried?

Even if many interesting similarities between the classical and the quantum mechanical framework have been worked out, e.g. in the subject of deformation quantization, in general, there are some ...
5
votes
1answer
16k views

What does $\Psi^*$ mean in Schrodinger's formulation of Quantum Mechanics?

I am not a physics student. In one of my courses, some fundamental concepts of Quantum mechanics were needed, so I was going through them when I stumbled upon this. It says $$\text{probability} = \...
5
votes
1answer
137 views

Atomic physics, determining levels and terms

In atomic physics I understand there a configurations, terms and levels. I think levels for instance appear because of spin-orbit interactions, so that terms are split. But I'm confused about the ...
3
votes
1answer
452 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 ...
2
votes
1answer
642 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 ...
2
votes
2answers
5k 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): ...
7
votes
2answers
3k views

Bra-Ket Notation

I'm having difficulty understanding the bra-ket notation used in quantum mechanics. For instance, take the notation used in the question Is there a relation between quantum theory and Fourier analysis?...
67
votes
10answers
5k views

Should zero be followed by units? [duplicate]

Today at a teachers' seminar, one of the teachers asked for fun whether zero should be followed by units (e.g. 0 metres/second or 0 metre or 0 moles). This question became a hot topic, and some ...
2
votes
2answers
3k 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) \...
18
votes
4answers
4k 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. Transcription: $...
4
votes
3answers
784 views

Dirac notation - specific acting orientation for operators

I have this doubt: Imagine two operators $A$ and $B$ and the state $\psi$. I know that the following statement is true: $$\langle\psi| A|\psi\rangle^*=\langle\psi| A^\dagger|\psi\rangle$$ But is ...
3
votes
1answer
1k views

Correct tetrad index notation

There seems to be some different conventions on the indexes of the tetrad. I am wondering which is the standard, which is correct, and which is an abuse of notation. In Sean Carroll's notes and in ...
3
votes
1answer
563 views

Why is not ${(\Lambda^T)^\mu}_\nu = {\Lambda_\nu}^\mu$?

I am following lecture notes on SR. The author writes that the following is equivalent: $$\Lambda^T\eta\Lambda = \eta \iff \eta_{\mu \nu} {\Lambda^\mu}_\rho{\Lambda^\nu}_\sigma = \eta_{\rho \sigma}. \...
3
votes
6answers
2k 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 \...
6
votes
2answers
888 views

A confusion about notation in Goldstein

On treating systems of particles, Goldstein starts with the consideration that whenever there are $k$ particles on a system, the $i$-th one obeys the relation $$\dfrac{d}{dt}{\bf p}_i = {\bf F}_i^{(e)...
5
votes
2answers
860 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. ...
2
votes
1answer
448 views

Arrow and flow of charge in fermion propagator

The momentum-space fermion propagator in the free Dirac theory is given by The arrow on the fermion propagator is said to represent the flow of charge. How can we derive this statement ...
7
votes
6answers
293 views

In quantum mechanics, is $|\psi\rangle$ equal to $\psi(x)$?

So I'm going through my notes and I think I've confused myself. We often imply $$ |\psi\rangle \to \psi(x)\\ \langle\psi| \to \psi(x)^* $$ for instance when we talk about eigenvalue equations we ...
3
votes
2answers
25k views

What does $\bar{y}$ 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 $\bar{y}$ with the line over it represent? And also, ...
1
vote
2answers
208 views

Operator in quantum mechanics

I'm really confused by the definition and uses of operators in quantum mechanics. Usually we say that the state of a system is described by some vector $\lvert\psi\rangle$ in a Hilbert space $H$, and ...
1
vote
2answers
312 views

What does $\partial_{\mu}$ mean?

I've stumbled across the following notation a couple times reading physics articles on wikipedia: $$\partial_{\mu}$$ But what does it mean? They don't clarify. Source: https://en.wikipedia.org/wiki/...
4
votes
3answers
771 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 ...
3
votes
1answer
245 views

$\delta$ differential notation

Various textbooks that I am currently consulting (including Spacecraft Dynamics and Control An Introduction - Anton H.J. De Ruiter | Christopher J. Damaren | James R. Forbes Section 1.4, page 32) use $...
1
vote
2answers
137 views

Why in the relativistic quantum mechanics $ \gamma_4$ name is not used instead of $ \gamma_5$?

I have seen in the in the Dirac equation $$\gamma_0,\gamma_1,\gamma_2,\gamma_3.$$ Then I have seen the definition of a new matrix $$\gamma_5=i\gamma_0\gamma_1\gamma_2\gamma_3.$$ Now my question is why ...
0
votes
1answer
196 views

Scalar Field Theories

The Lagrangian density for a single real scalar field theory is \begin{equation}\mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)^{2}-V(\phi)\end{equation} I have often seen this written \begin{equation}\...
0
votes
1answer
121 views

Axis/vector notation in Minkowski diagrams

Learning special relativity and working with Minkowski diagrams for a while now i am still trying to get my head around some oddity. From my understanding time can often be seen as the dependent ...