Abstract
Abstract
We apply a recent formalism of quantum geodesics to the well-known quantum Minkowski spacetime [x
i
, t] = ıλ
p
x
i
with its flat quantum metric as a model of quantum gravity effects, with λ
p
the Planck scale. As examples, quantum geodesic flow of a plane wave gets an order λ
p
frequency dependent correction to the classical geodesic velocity. A quantum geodesic flow with classical velocity v of a Gaussian with width
2
β
initially centred at the origin changes its shape but its centre of mass moves with
⟨
x
⟩
⟨
t
⟩
=
v
(
1
+
3
λ
p
2
2
β
+
O
(
λ
p
3
)
)
, an order
λ
p
2
correction. This implies, at least within perturbation theory, that a ‘point particle’ cannot be modelled as an infinitely sharp Gaussian due to quantum gravity corrections. For contrast, we also look at quantum geodesics on the noncommutative torus with a 2D curved weak quantum Levi-Civita connection.
Funder
China Scholarship C/O of Queen Mary University of London
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
4 articles.
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