Abstract
We find a coordinate-independent wave-packet solution of the massive Klein–Gordon equation with the conformal coupling to gravity in the de-Sitter universe. This solution can locally be represented through the superposition of positive-frequency plane waves at any space-time point, assuming that the scalar-field mass M is much bigger than the de-Sitter Hubble constant H. The solution is also shown to be related to the two-point function in the de-Sitter quantum vacuum. Moreover, we study the wave-packet propagation over cosmological times, depending on the ratio of M and H. In doing so, we find that this wave packet propagates like a point-like particle of the same mass if M ggg H, but, if otherwise, the wave packet behaves highly non-classically.
Highlights
Elementary particles in Minkowski spacetime are related to unitary and irreducible representations of the Poincaré group
It is evident though that it is impossible to carry out a scattering experiment with the asymptotic states, i.e. states defined at t → ±∞, in collider physics, bearing in mind that initial states should have been arranged at the Big Bang. This apparent tension between theoretical constructions and experiments can be eliminated by taking into account that elementary particles are quantum-field excitations localised in spacetime, namely they are described by wave packets with a finite space-time extent
Elementary particles are described by wave packets in quantum theory
Summary
Elementary particles in Minkowski spacetime are related to unitary and irreducible representations of the Poincaré group. The electron neutrino was foreseen in β-decay from energy–momentum conservation long before its actual detection [5] These conservation laws are, in turn, related to the space-time translation and rotational symmetries which are spontaneously broken in nature. It is an empirical fact that particles in collider physics are well defined, even though the observable Universe is evolving This could be readily explained if wave functions, which describe particles, are well localised in spacetime. Their nonpoint-like support is still testable in gravity, namely the quantum interference of non-relativistic neutrons was observed in the Earth’s gravitational field [7].
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