# 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.

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### Why do we use down and up arrows? [closed]

Using electron Quantum Superposition, electrons exist as a superposition of their different spin states (-1/2 and +1/2). If so, apart from simplicity is there any other reason we use the up and down ...
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### Why is the notation/convention of the equation for an electron scattering event $e−e−→e−e−$ rather than $e−+e−→e−+e−$? [closed]

I'm trying to help out my son who is attempting year 12 physics. They have to cover Lepton and Baryon conservation, and understand 5 Feynman diagrams - Moller scattering, Bhabha scattering, electron-...
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### How to go from usual vector/matrix notation to weyl spinor notation?

I've always had trouble understanding the notation with dots, also known as the notation for Weyl spinors or Van der Waerden notation. I would like to ask for help. For example, (Becker-Becker, page ...
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### Why we have $|P\rangle =\int dp \space |p\rangle p \langle p| =-i\hbar \int dx |x\rangle \frac{d}{dx} \langle x|$?

And similarly, why we have $$\langle x|P|x' \rangle =-i\hbar \frac{d}{dx} \delta(x-x')~?$$ Both equations come from the Wikipedia page Momentum operator. My question is, if we insert the identity ...
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### Occupation number doubt in QFT [closed]

Let say we have the Hamiltonian of a free scalar field in QFT: $$\hat{H} = \mathcal{V}\int{\frac{d^3k}{8\pi^3}\hbar\omega_k\left(\hat{a}^\dagger_k\hat{a}_k+\frac{1}{2}\right)}$$ The question is what ...
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### Position Eigenstate and Parity Operator

I would like to ask for help with a question that I can't solve. I know that in quantum mechanics an abstract state $|x\rangle$ (position) is defined up to a phase $e^{i\theta}|x\rangle$. Now we know ...
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### Symbol denoting parity eigenvalue

What is the symbol reserved for designating the parity of a parity eigenstate? For example an eigenstate $\phi$ of the squared angular momentum operator $\hat{\mathbf{L}}^2$ is characterized by a ...
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### Dirac's Bracket Notation

I have a question on Dirac's bracket notation. In particular, according to this notation, vectors and covectors are represented by $|\psi\rangle$ and $\langle\psi|$ respectively. Moreover, these two ...
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### Operator's definition in Dirac picture [closed]

I have a question about the definition of quantum operators in the Dirac picture. The definition is: $$A=\sum_i \sum_j \vert i \rangle A_{ij} \langle j \vert.\tag{1}$$ By deplacing the ket vector I ...
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1 vote
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### What does it mean when vector quantity is negative?

I’ve seen in some problems that vector quantity is negative. For example, negative Coulomb means that two charges attract… negative acceleration means that object is slowing down. However, magnitude ...
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### What does $v$ actually represent in pulley problems?

Let us consider the problem of two pulleys with boxes attached to their ends. One pulley is movable, and the other is not. The problem requires us to find a relationship between velocities of these ...
1 vote
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### About the notation for TEM waves

I just came across this article where the term "$\mathrm{TE}_{101}$ microwave mode" is mentioned. Other than the basics of TEM waves which I learned in Griffiths, this is the first time I ...
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### What's the difference? $\nabla_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~\text{ and }~\partial_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~?$

What's the difference? $$\nabla_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~\text{ and }~\partial_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~?$$ In John Dirk Walecka's book 'Introduction to General Relativity',...
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### Multiplication of $\mathrm{U}(3)$ matrices [closed]

On this page of this paper: I am unable to understand how they multiplied the $3\times 3$ $\mathrm{U}(3)$ matrix with $T_{3,2}$, which is a $2\times 2$ matrix, in Eqs. (26) to (28). Can anyone please ...
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### What does the superscript $3$ in $d^3x$ mean in an integral?

At the risk of seeming ignorant, please explain what does the superscript $3$ in $d^3x$ mean in the integrals 5.12, 5.13, 5.14, 5.15? Why 3? Why there is no such in the 5.10 integral?
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### What is $r$ in a metric signature in general relativity? If $v$ and $p$ are the time and spatial coordinates?

The Wikipedia article on metric signatures says that the signature of a metric can be written $(v,p,r)$, where $v$ is the number of positive eigenvalues, $p$ is the number of negative eigenvalues, and ...
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1 vote
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### Would it be valid to say $y \propto 2x$ instead of $y \propto x$?

Would it be acceptable to write $y \propto 2x$ or would it be wrong to add the $2$? I just want to describe a relationship in more detail.
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### Complex coordinates $ds^2 = dzdz̄$ in 2d
I have a very elementary question about complex coordinates in two dimensions. When we have a 2D Euclidean space, $$ds^2 = dx^2 +dy^2$$ and we go to complex coordinates: $$z = x + iy$$ $$z̄ = x - iy$$ ...