Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hardy-Lieb-Thirring Inequalities for Fractional Pauli Operators   We provide lower bounds for the sum of the negative eigenvalues of the
operator $|\sigma\cdot p_A|^{2s} - C_s/|x|^{2s} + V$ in three dimensions, where
$s\in (0, 1]$, covering the interesting physical cases $s = 1$ and $s = 1/2$.
Here $\sigma$ is the vector of Pauli matrices, $p_A = p - A$, with $p =
-i\nabla$ the three-dimensional momentum operator and $A$ a given magnetic
vector potential, and $C_s$ is the critical Hardy constant, that is, the
optimal constant in the Hardy inequality $|p|^{2s} \geq C_s/|x|^{2s}$. If spin
is neglected, results of this type are known in the literature as
Hardy-Lieb-Thirring inequalities, which bound the sum of negative eigenvalues
from below by $-M_s\int V_{-}^{1 + 3/(2s)}$, for a positive constant $M_s$. The
inclusion of magnetic fields in this case follows from the non-magnetic case by
diamagnetism. The addition of spin, however, offers extra challenges that make
the result more elusive. It is the purpose of this article to resolve this
problem by providing simple bounds for the sum of the negative eigenvalues of
the operator in question. In particular, for $1/2 \leq s \leq 1$ we are able to
express the bound purely in terms of the magnetic field energy $\|B\|_2^2$ and
integrals of powers of the negative part of $V$.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
1
The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat