Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connes spectral distance and nonlocality of generalized noncommutative
  phase spaces   We study the Connes spectral distance of quantum states and analyse the
nonlocality of the $4D$ generalized noncommutative phase space. By virtue of
the Hilbert-Schmidt operatorial formulation, we obtain the Dirac operator and
construct a spectral triple corresponding to the noncommutative phase space.
Based on the ball condition, we obtain some constraint relations about the
optimal elements, and then calculate the Connes spectral distance between two
Fock states. Due to the noncommutativity, the spectral distances between Fock
states in generalized noncommutative phase space are shorter than those in
normal phase space. This shortening of distances implies some kind of
nonlocality caused by the noncommutativity. We also find that these spectral
distances in $4D$ generalized noncommutative phase space are additive and
satisfy the normal Pythagoras theorem. When the noncommutative parameters equal
zero, the results return to those in normal quantum phase space.

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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
27
The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: nlin