Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Covariant Quantum Mechanics and Quantum Spacetime   We present in the article the formulation of a version of Lorentz covariant
quantum mechanics based on a group theoretical construction from a
Heisenberg-Weyl symmetry with position and momentum operators transforming as
Minkowski four-vectors under the Lorentz symmetry. The basic representation is
identified as a coherent state representation, essentially an irreducible
component of the regular representation, with the matching representation of an
extension of the group $C^*$-algebra giving the algebra of observables. The key
feature of the formulation is that it is not unitary but pseudo-unitary,
exactly in the same sense as the Minkowski spacetime representation. Explicit
wavefunction description is given without any restriction of the variable
domains, yet with a finite integral inner product. The associated covariant
harmonic oscillator Fock state basis has all the standard properties in exact
analog to those of a harmonic oscillator with Euclidean position and momentum
operators of any `dimension'. Galilean limit of the Lorentz symmetry and the
classical limit of the Lorentz covariant framework are retrieved rigorously
through appropriate symmetry contractions of the algebra and its
representation, including the dynamics described through the symmetry of the
phase space, given both in terms of real/complex number coordinates and
noncommutative operator coordinates. The latter gives an explicit picture of
the (projective) Hilbert space as a quantum/noncommutative spacetime.

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The categories of this paper are: dg-ga
18
The categories of this paper are: econ
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con