Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classical and Quantum Fermions Linked by an Algebraic Deformation   We study the regular representation $\rho_\zeta$ of the single-fermion
algebra ${\cal A}_\zeta$, i.e., $c^2=c^{+2}=0$, $cc^++c^+c=\zeta~1$, for
$\zeta\in [0,1]$. We show that $\rho_0$ is a four-dimensional nonunitary
representation of ${\cal A}_0$ which is faithfully irreducible (it does not
admit a proper faithful subrepresentation). Moreover, $\rho_0$ is the minimal
faithfully irreducible representation of ${\cal A}_0$ in the sense that every
faithful representation of ${\cal A}_0$ has a subrepresentation that is
equivalent to $\rho_0$. We therefore identify a classical fermion with $\rho_0$
and view its quantization as the deformation: $\zeta:0\to 1$ of $\rho_\zeta$.
The latter has the effect of mapping $\rho_0$ into the four-dimensional,
unitary, (faithfully) reducible representation $\rho_1$ of ${\cal A}_1$ that is
precisely the representation associated with a Dirac fermion.

20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga