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

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 behavior under Lorentz boosts. We calculate the decay rate of a particle of mass M modeled as a Gaussian wave packet of width a and centered at zero momentum. We find the decay rate to be Gamma 0[1 - 4M3a22 + O(Ma44)], where Gamma 0 is the decay rate of the particle at rest treated as a plane wave. The leading correction is then of orderMa22. We then perform a Lorentz boost of velocity v on the above Gaussian and find that its decay rate does not decrease exactly by the Lorentz factor 1 - v2. There is a correction of order a2v2 wave packet does not act exactly like a typical clock under Lorentz boosts, and we refer to it is a WP clock (wave packet clock). A WP clock does not move with a single velocity relative to an observer but has a spread in velocities (more specifically, a spread in momenta). Nonetheless, it is best viewed as a single clock as the wave packet represents a one-particle state in QFT. WP clocks do not violate Lorentz symmetry and are not based on new physics; they are a consequence of the combined requirements of special relativity, quantum mechanics, and localized free particles.

Automated summary

This study discusses the effects of using wave packets to represent localized free particles on decay rates and clock behavior in quantum field theory. It is found that a wave packet clock does not behave exactly like a typical clock under Lorentz boosts, with its velocity having a spread. However, the wave packet clock represents a one-particle state in QFT and does not violate Lorentz symmetry, as it is a consequence of the requirements of special relativity, quantum mechanics, and localized free particles.