Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical Assemblies of Particles with Spin   Spin, $s$ in quantum theory can assume only half odd integer or integer
values. For a given $s$, there exist $n=2s+1$ states $|s,m\rangle$,
$m=s,s-1,........,-s$. A statistical assembly of particles (like a beam or
target employed in experiments in physics) with the lowest value of spin
$s=\frac {1}{2}$ can be described in terms of probabilities $p_m$ assigned to
the two states $m=\pm \frac {1}{2}$. A generalization of this concept to higher
spins $s>\frac {1}{2}$ leads only to a particularly simple category of
statistical assemblies known as `Oriented systems'. To provide a comprehensive
description of all realizable categories of statistical assemblies in
experiments, it is advantageous to employ the generators of the Lie group
$SU(n)$. The probability domain then gets identified to the interior of regular
polyhedra in $\Re^{n-1},$ where the centre corresponds to an unpolarized
assembly and the vertices represent `pure' states. All the other interior
points correspond to `mixed' states. The higher spin system has embedded within
itself a set of $s(2s+1)$ independent axes, which are determinable empirically.
Only when all these axes turn out to be collinear, the simple category of
`Oriented systems' is realized, where probabilities $p_m$ are assigned to the
states $|s,m\rangle$. The simplest case of higher spin $s=1$ provides an
illustrative example, where additional features of `aligned' and more general
`non oriented' categories are displayed.

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The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat