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

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Summary

Introduction

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].

Adiabatic particles in de-Sitter spacetime
Motivation
Covariant wave packet in Minkowski spacetime
Gaussian wave packet in Minkowski spacetime
Wave-packet position in Minkowski spacetime
Wave-packet momentum in Minkowski spacetime
Covariant wave packet in de-Sitter spacetime
Locally plane-wave solutions in de-Sitter spacetime
In-in and in-out propagators in de-Sitter spacetime
Gaussian wave packet in de-Sitter spacetime
Wave-packet position in de-Sitter spacetime
Wave-packet position and momentum in co-moving frame
Discussion

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