Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probing the Planck scale: The modification of the time evolution
  operator due to the quantum structure of spacetime   The propagator which evolves the wave-function in NRQM, can be expressed as a
matrix element of a time evolution operator: i.e $ G_{\rm NR}(x)=
\langle{\mathbf{x}_2}|{U_{\rm NR}(t)}|{\mathbf{x}_1}\rangle$ in terms of the
orthonormal eigenkets $|{\mathbf{x}}\rangle$ of the position operator. In QFT,
it is not possible to define a conceptually useful single-particle position
operator or its eigenkets. It is also not possible to interpret the
relativistic (Feynman) propagator $G_R(x)$ as evolving any kind of
single-particle wave-functions. In spite of all these, it is indeed possible to
express the propagator of a free spinless particle, in QFT, as a matrix element
$\langle{\mathbf{x}_2}|{U_{\rm R}(t)}|{\mathbf{x}_1}\rangle$ for a suitably
defined time evolution operator and (non-orthonormal) kets
$|{\mathbf{x}}\rangle$ labeled by spatial coordinates. At mesoscopic scales,
which are close but not too close to Planck scale, one can incorporate quantum
gravitational corrections to the propagator by introducing a zero-point-length.
It turns out that even this QG corrected propagator can be expressed as a
matrix element $\langle{\mathbf{x}_2}|{U_{\rm QG}(t)}|{\mathbf{x}_1}\rangle$. I
describe these results and explore several consequences. It turns out that the
evolution operator $U_{\rm QG}(t)$ becomes non-unitary for sub-Planckian time
intervals while remaining unitary for time interval is larger than Planck time.
The results can be generalised to any ultrastatic curved spacetime.

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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
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The categories of this paper are: q-fin
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph