Wave packets in QFT: leading order width corrections to decay rates and clock behaviour under Lorentz boosts

Abstract

Decay rates in quantum field theory (QFT) are typically calculated assuming the particles are represented by momentum eigenstates (i.e. plane waves). However, strictly speaking, localized free particles should be represented by wave packets. This yields width corrections to the decay rate and to the clock behaviour under Lorentz boosts. We calculate the decay rate of a particle of mass M modeled as a Gaussian wavepacket of width a and centered at zero momentum. We find the decay rate to be Γ 0 1 − 3a 2 4M 2 + O a 4 M 4 *