question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings sequencelengths 768 768 |
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<p>Let's discuss about $SU(3)$. I understand that the most important representations (relevant to physics) are the defining and the adjoint. In the defining representation of $SU(3)$; namely $\mathbf{3}$, the Gell-Mann matrices are used to represent the generators
$$
\left[T^{A}\right]_{ij} = \dfrac{1}{2}\lambda^{A},... | g1039 | [
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<p>So in the context of a set of notes I am reading about acoustics I get to equation (23) in this <a href="http://www3.nd.edu/~atassi/Teaching/ame%2060639/Notes/fundamentals_w.pdf" rel="nofollow">paper</a>. Basically it comes down to showing that (<strong>note the dots above the a's meaning time derivative!)</strong><... | g1040 | [
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<p>I was wondering with a question for a quite long time, thought to ask here.</p>
<p>I need to know is there any material or element which can block magnetic field? I mean I am searching for such material or element that cannot allow magnetic field though itself?</p>
<p>The practical scenario is, there are two perma... | g0 | [
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<p>Why is the gravitation force always attractive? Is there a way to explain this other than the curvature of space time? </p>
<p>PS: If the simple answer to this question is that mass makes space-time curve in a concave fashion, I can rephrase the question as why does mass make space-time always curve with concavity?... | g81 | [
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<p>I am wondering what will be the physics to explain how two neutral, chemically nonreactive objects stick. I know that using van der Waals formalism, we can treat neutral body electrodynamic forces and arrive with attractive forces that pull the objects together. </p>
<p>Now, once the objects touch (say a mechanical... | g1041 | [
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<p>I have a question about the relation:
$\exp(-i \vec{\sigma} \cdot \hat{n}\phi/2) = \cos(\phi/2) - i \vec{\sigma} \cdot \hat{n} \sin(\phi/2)$.</p>
<p>In my texts, I see $\phi\hat{n}$ always as c-numbers. My question is whether or not this relation can be generalized for $\hat{n}$ being an operator?</p>
<p>If so how... | g1042 | [
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<p>The second postulate of <a href="http://en.wikipedia.org/wiki/Special_relativity" rel="nofollow">special relativity</a> deals with constancy of light in inertial reference frames. But, how did Einstein came to this conclusion? Did he knew about the <a href="http://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_exper... | g1043 | [
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<p>Does one need to invoke quantum mechanics to explain casimir force or vander waals force. I see that textbooks show derivation of vander waal force with no QM but casimir force is typically described with QM. </p>
<p>Is there a difference between vanderwaal and casimir forces ? Are there distinct examples of these ... | g1044 | [
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<p>Einstein has suggested that light can behave as a waves as well as like a particle i.e, it has dual character. In 1924, Louis de Broglie suggested that just as light exhibits wave and particle properties, all microscopic material particles such as electrons, protons, atoms, molecules etc. have also dual character. T... | g1 | [
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<p>When studying the de Broglie relations, I have stumbled across the following problem:</p>
<blockquote>
<p>Consider an electron with known velocity $v$ and assume: $v \ll c$. Calculate the corresponding wavelength of the electron.</p>
</blockquote>
<p>Using the de Broglie relations from Wikipedia:
$$\begin{align}... | g2 | [
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<p>Are there any known uses of modeling with elastic fractals in current physical applications? (Especially uses concerning with self-similarity)</p> | g1045 | [
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