Questions tagged [notation]
This tag is for questions on the meaning, history, and usage of various symbols and notation that are used to denote different quantities in physics. Don't forget to mention the reference, where you encountered those notations.
1,637
questions
1
vote
2
answers
110
views
A question about a comment from Byron and Fuller, pg 533
Seeing the equation,
\begin{equation*} (\hat{A} -\lambda)G_\lambda
(\mathbf{x},\mathbf{y})=\delta^{(3)}(\mathbf{x}-\mathbf{y}) \tag{1}
\end{equation*}
in the answer
What is different between ...
1
vote
1
answer
71
views
Bianchi identity contradiction in Abelian case
In non-abelian gauge theory, such as P & S's chapter 15, eq. (15.89), we also have Bianchi identity.
Start with
$$\epsilon^{\mu\nu\lambda\sigma}[D_\nu,[D_\lambda,D_\sigma]]=0$$
and use $[D_\mu,D_\...
1
vote
1
answer
46
views
Expectation value of potential operator [closed]
A book says $$\langle r|V|r\rangle$$=$$\sum_{a,a'}\int \psi^*_a(r)V_{aa'}\psi_{a'}(r) $$
define $$\langle r|\psi\rangle=\psi(r)$$
my derivation is $$\langle r|V|r\rangle=\langle r|\psi_a\rangle\...
1
vote
1
answer
98
views
Suppressed indices - when and why?
When following textbooks in QFT I have many times seen the usage of 'suppressed indices'. This is a bit confusing to me, sometimes it is done without any explanation. For instance I usually see that ...
1
vote
1
answer
89
views
What is the difference whether a space is used between number and unit for temperature? [closed]
When talking about temperature, or temperature change, -32.5 ℃ (with space), and -32.5℃ (no space) are two common expressions. Are they the same?
If there is no space is used, there is a problem about ...
1
vote
1
answer
143
views
Equation 7.16 Susskind Theoretical Minumum Quantum Mechanics
Could someone explain/expand equation \eqref{7.16} from Susskind's "Quantum Mechanics-The Theoretical Minimum" in particular, what are the indexes $a',a$ in the operator $\,\mathbf L\,$ ...
1
vote
1
answer
59
views
What does $\sin(a,b)$ mean in the absorber theory of radiation?
I'm doing a revision of the absorber theory of radiation by Wheeler and Feynman (that you can see here: "Interaction with the Absorber as the Mechanism of Radiation" - page 161) and I have ...
1
vote
1
answer
624
views
Divergence theorem in index notation
From Batchelor's book of fluid dynamics:
I guess that's an easy question for anyone having more familiartiy than me in tensor calculus, anyways.
First integral argument is the i-component of the ...
1
vote
2
answers
346
views
What is $M_N$ in the Goldberger-Treiman relation?
$$g_{\pi NN} F_\pi = G_A M_N .$$
Does it stand for the magnetic moment of the neutron?
One place I came across it was on Wikipedia, on their QCD Vacuum page, in the section about experimental evidence,...
1
vote
1
answer
198
views
How to make notation like $Y_{l m_{l}}(\theta, \phi)\chi_{m_s}$ more rigorous as a tensor product?
Sometimes in quantum mechanics we come across notation like $Y_{l m_{l}}(\theta, \phi)\chi_{sm_s}$ where $Y_{lm_l}$ is a spherical harmonic representing the spatial part of some particle wavefunction ...
1
vote
1
answer
238
views
How is the projection operator derived?
I am having a difficult time understanding how do we go from
$$ C_{n}=\langle n | \psi\rangle $$
and
$$ \psi=\sum C_{n}|\psi\rangle$$
to
$$ \psi=\left(\sum |n\rangle\ \langle n| \right) |\psi \rangle.$...
1
vote
1
answer
95
views
Action of permutation operator on other operators
I'm watching MIT 8.06 Quantum physics, lecture $23.2$ See for example [1] Particularly See $5:41$. It is shown that
$$P_{21}B(1)P^\dagger_{21}|u_i\rangle_1\otimes |u_j\rangle_2=|u_i\rangle_1\otimes |...
1
vote
1
answer
42
views
A notational confusion in a Bell-type inequality
In the tripartite Bell-type inequality know as Svetlichny inequality, given in this (freely available) article. The quantity $M_{ijk} = Tr [\rho(\sigma_i \otimes \sigma_j \otimes \sigma_k)]$, $i,j,k\...
1
vote
1
answer
163
views
How to express a $u$-substitution in Dirac notation?
Suppose I have a set of functions $g=g(x)$, that form a basis in the Hilbert Space. I can define states $|g\rangle$ associated with this basis.
Suppose I have some integral in the $x$ basis. I can ...
1
vote
1
answer
142
views
Different adjoints in particle physics
I am currently reading Quantum Chromodynamics on the Lattice by C. Gattringer C.B. Lang and I am confused about an expression in the book.
The expression is
$$\langle \text{tr}[S(\textbf{m}, \textbf{n}...
1
vote
1
answer
51
views
Electrostatic boundary conditions notation
In one book example we are trying to find the electric potential of a infinite long steel bar that is homogeneously charged that has a radius $R$. And We will be using the discontinuity of the normal ...
1
vote
1
answer
182
views
Problem in understanding notation of scattering amplitude
The Schrodinger equation: $$
i \frac{d}{d t}\left|\psi_{t}\right\rangle=H\left|\psi_{t}\right\rangle
$$
and solutions are given by
$$\left|\psi_{t}\right\rangle=U(t)|\psi_\text{in}\rangle \equiv e^{-...
1
vote
1
answer
180
views
Understanding covariant and contravarient components of vector in Ket notation
I learned about covariant and contravariant vectors in the context of Vector and Tensor analysis and Now I'm learning about it in the context of Linear vector spaces in Dirac ket notation. I'm having ...
1
vote
1
answer
67
views
What is the apostrophe I see in HEP articles? (NOT antiquark)
I keep seeing references to quarks as q, and antiquarks as qbar, but I'm also seeing things like q' and q'bar. I originally thought it was another form of notation for anti- but it doesn't appear like ...
1
vote
1
answer
115
views
Strong equality in Quantization of Gauge Systems by Henneaux and Teitelboim
I am new to the concept of weak and strong equalities, and I have a doubt trying to derive an expression.
In section $1.2.1$ of Henneaux and Teitelboim's Quantization of Gauge Systems, there is a ...
1
vote
1
answer
210
views
Raising and lowering indices in quantum field theory
Is raising and lowering indices in quantum field theory works the same as in the general theory of relativity?
By means of this metric tensor?
$$g^{μν}=
\begin{pmatrix}
1 & 0 & 0 & 0\\
...
1
vote
1
answer
136
views
Can anyone expound this Projectile Motion computation please?
I have this formula for projectile motion that I'm using in Unity game engine for getting the low or high Velocity of a projectile depending on how close or distant the target is (as long as it is ...
1
vote
2
answers
72
views
$\sin$ with angle subscript
In reading Haar's book on the old quantum mechanics, I came across a derivation of the square of the (classical) angular momentum that I am having some trouble understanding.
He claims that the square ...
1
vote
1
answer
41
views
Notation for the position and momentum differentials in a system of $N$ particles and $d$ dimensions
I am a little confused with the notation used in Statistical Mechanics for the differentials of position and momentum in the phase space. For instance, I have found different notations in different ...
1
vote
1
answer
81
views
Deriving uncertainty relation between operators (Zettili)
Zettili's Quantum Mechanics, section 2.4.5 (p95):
$\hat A$ is an operator and $\langle\hat A\rangle$ is its expectation value with respect to a normalized state vector. Then the operator $\Delta \hat ...
1
vote
2
answers
285
views
Notations related to identities for spinors in the rest frame
This question pertains to some notation in Zee's QFT book, Section II.2. The Dirac equation is
$$ (i\gamma^\mu\partial_\mu-m)\psi(x)=0, $$
which we can write in momentum space with the Fourier ...
1
vote
1
answer
355
views
Proof of volume density transformation under infinitesimal diffeomorphisms using Levi-civita/ determinant
Given I diffeomorphism $x^\mu \rightarrow y^\mu = y^\mu(x) $, I want to show that the volume density is invariant, i.e. $ \sqrt{-g(x)}\,\mathrm d^4x \rightarrow \sqrt{-g(y)}\,\mathrm d^4y $. The ...
1
vote
1
answer
83
views
Killing vector index manipulation
I was doing some problems of the book "Problem Book in Relativity and Gravitation by A. Lightman, R. H. Price" and on problem 10.14 I dont understand why they say:
$\xi^{}_{\gamma;\beta}\xi^{...
1
vote
1
answer
1k
views
Nomenclature of X-ray transitions-Siegbahn Notation
A colleague wanted to understand the notation for X-ray transitions. The main query is about the labeling of alpha, beta and gamma, with K, L, M etc. What is the main distinguishing criterion to label ...
1
vote
1
answer
36
views
Is it okay to for the integrand and bounds of integration to be functions of the same variable?
For the sake of simplicity, say we given that $a = 6t$ and that we must find the velocity as a function of time. We would set up the following integral:
$$\displaystyle \int_{v(t_0)}^{v(t)}dv = \int_{...
1
vote
3
answers
5k
views
Expectation Value in Bra-ket notation
I've been staring at this problem for quite sometime, but I don't think I understand bra-ket notation in the form $<a | x | a>$. I understand that <a|x> is just an inner product, but I ...
1
vote
1
answer
58
views
I don't know why i can't use this equation (in the pic) in flatspace, I'm learning general relativity (metric tensor)
I don't know why this equation cannot be used in flatspace, Who can help me?
1
vote
1
answer
141
views
Notation for vector time derivatives [closed]
So I am self-studying mechanics using Marion and, as many books, it uses the notation of the dot over the function to express a time derivative, as in
$$x = x(t)$$
$$\dot{x}= \frac{dx}{dt}(t) $$
The ...
1
vote
1
answer
152
views
Can value of the variable be substituted in partial derivatives before taking the derivative?
I was going through the D'Alembert's solution for the wave equation using this pdf from University of British Columbia (UBC, Canada). Here's the link: https://www.math.ubc.ca/~ward/teaching/m316/...
1
vote
1
answer
98
views
Notation in 'right/left moving' modes
In Superstring Theory Vol.1 chapter 2.1 we define the general solution to the massless wave equation:
$$
X^\mu(\sigma)=X^\mu_R(\sigma^-)+X^\mu_R(\sigma^+)
$$
with $$
\sigma^- = \tau-\sigma
$$
$$
\...
1
vote
1
answer
104
views
Completeness relation, commuting operators
I have a question about some formulars our professor wrote on the black board.
Let $\hat{Q}_{1},...,\hat{Q}_{N}$ be operators, which are a CSCO. We know now that there exists a set of eigenvectors $\{...
1
vote
1
answer
127
views
Question about computing Christoffel symbols
I am trying to calculate the Christoffel symbols in polar coordinates, and I am confused on one step. Given that I am here, for example:
$$\Gamma_{r \theta}^{\theta}=\frac{1}{2} g^{\alpha \theta}\...
1
vote
3
answers
1k
views
Quantum Field Theory: Number Operator $\hat{N} = a^\dagger a$ and bra-ket notation
My textbook, Quantum Field Theory and the Standard Model by Schwartz, says the following:
The easiest way to study a quantum harmonic oscillator is with creation and annihilation operators, $a^\...
1
vote
1
answer
66
views
Is this a projection of a tensor state?
Take the state $|\Psi\rangle $ living in a product space of space 1 and space 2 with orthonormal bases $\varphi,\phi $ $$|\Psi\rangle=\sum_{i,j}a_ib_j|\varphi_i\rangle\otimes|\phi_j\rangle $$
Is the ...
1
vote
1
answer
296
views
Virasoro Algebra commutation
In Introduction to Conformal Field Theory by Blumenhagen and Plauschinn (springer link) the Virasoro algebra is introduced the central extension of the Witt algebra. They give the central extension $$\...
1
vote
1
answer
244
views
What is the meaning of $d$? [duplicate]
What is the meaning of $d$? Is is Delta? If it is Delta, why is it then not $\Delta$? I am still confused with that. Can someone help explain it to me?
1
vote
1
answer
79
views
Question about explicit notation of averaged energy conditions integrals
Beyond the basics of general relativity, we rapid encounter the so called Averaged energy conditions. The mathematics of these quantities are related to line and volume integrals.
As given by [1], ...
1
vote
1
answer
250
views
Simple explanation of a particular diagrams of Feynman [closed]
In relation to this question posed on the website TeX.SE. I am curious to know the use in Physics of green functions about the signs of feynman diagrams with fermionic fields.
I have not understood ...
1
vote
1
answer
2k
views
What does degeneracy and multiplicity in Term symbol mean?
$^{2S+1}L_J$ was the term symbol.
I watched a video online saying $2J+1$ was the fold of degeneracy to the term symbol.
Specifically, for nitrogen, the term symbol for the lowest energy was $^4S_{3/...
1
vote
2
answers
184
views
When is the order of magnitude not equal to the exponent of scientific notation?
Explain why the order of magnitude is sometimes not the same as the exponent in scientific notation. It is because of the units?
1
vote
1
answer
69
views
Math notation for heating object
An object with mass $m$ and heat capacity $c_{p}$ is exposed to heating $P_{th} $[kW] and thermal losses $\dot q$ [kW/°C]. The energy equation illustrating the process of heating it from $T_{max}$ to $...
1
vote
1
answer
108
views
How to differentiate Capacitance (Italized C) and Coloumbs (regular C) on paper [closed]
I am doing a question on capacitance and coulombs. I got the answer correct, but I was wondering how a physicist, when doing the calculation on paper, would differentiate a C and C?
1
vote
1
answer
558
views
Peskin and Schroeder: derivation of Dirac fields commutator
I'm perplexed by the following non numbered equation at page 54 of Peskin & Schroeder, right between $(3.92)$ and $(3.93)$
$$ [\psi_a(x),\overline{\psi}_b(x)]=\int\frac{d^3p}{(2\pi)^3}\frac{1}{...
1
vote
1
answer
79
views
Electrodynamics : Problem with Notations for fields $\vec{(\vec{r},t)}$ and $\vec{B}(\vec{r},t)$(complex and real notations)
I'm sutyding a course on electrodynamics and am stuck on a few lines I can't make sense of. The professor uses $$\vec{E}(\vec{r},t) = \vec{U_0} cos (\vec{k}\cdot \vec{r} - \omega t + \phi)$$ (so far, ...
1
vote
2
answers
594
views
Covariant and contravariant coordinates - index notation
I am learning about electrodynamics and have recently been introduced to the four vector. I also come fresh to the idea of covariant four vectors and contravariant four vectors.
My question concerns ...