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.

Filter by
Sorted by
Tagged with
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 ...
user151522's user avatar
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_\...
Daren's user avatar
  • 1,401
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\...
MathJacky's user avatar
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 ...
Tjommen's user avatar
  • 301
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 ...
ChuaJia Cai's user avatar
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 $\,\mathbf L\,$ ...
David's user avatar
  • 21
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 ...
Pedro's user avatar
  • 45
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 ...
Osvaldo Paniccia's user avatar
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,...
Kurt Hikes's user avatar
  • 4,373
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 ...
Jagerber48's user avatar
  • 13.9k
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.$...
Basheer Algohi's user avatar
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 |...
Young Kindaichi's user avatar
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\...
user avatar
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 ...
Nakshatra Gangopadhay's user avatar
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}...
ColourConfined's user avatar
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 ...
imbAF's user avatar
  • 1,342
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^{-...
amilton moreira's user avatar
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 ...
Young Kindaichi's user avatar
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 ...
paula.b2's user avatar
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 ...
AFG's user avatar
  • 2,256
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\\ ...
Peter's user avatar
  • 367
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 ...
user1865775's user avatar
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 ...
Flumpo's user avatar
  • 173
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 ...
Invenietis's user avatar
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 ...
user avatar
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 ...
hodop smith's user avatar
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 ...
ZacharyC's user avatar
  • 194
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^{...
MicrosoftBruh's user avatar
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 ...
AChem's user avatar
  • 297
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_{...
DevrimA's user avatar
  • 108
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 ...
Kayla Kornoelje's user avatar
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?
I'm a lightbulb's user avatar
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 ...
Johnn.27's user avatar
  • 418
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/...
user115625's user avatar
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 $$ \sigma^- = \tau-\sigma $$ $$ \...
twisted manifold's user avatar
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 $\{...
B.Hueber's user avatar
  • 844
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}\...
user avatar
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^\...
The Pointer's user avatar
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 ...
Hans Wurst's user avatar
  • 1,535
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 $$\...
Vangi's user avatar
  • 592
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?
user avatar
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], ...
M.N.Raia's user avatar
  • 3,075
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 ...
Sebastiano's user avatar
  • 2,529
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/...
ShoutOutAndCalculate's user avatar
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?
CountDOOKU's user avatar
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 $...
cheesus's user avatar
  • 117
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?
mjj's user avatar
  • 53
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}{...
user2723984's user avatar
  • 4,686
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, ...
DeltaXY's user avatar
  • 11
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 ...
PhysicsMathsLove's user avatar

1
16 17
18
19 20
33