Mean propagation velocity of multiphoton wave-packet states with nonzero Lorentz-invariant mass

TL;DR

This paper investigates the Lorentz-invariant mass and mean propagation velocity of multiphoton wave-packet states, demonstrating that velocity is less than the speed of light and depends on the wave-vector space geometry.

Contribution

It provides a rigorous proof linking mean propagation velocity with Lorentz-invariant mass for multiphoton states and introduces modes to classify states by mass.

Findings

Mean propagation velocity is less than the speed of light.

Velocity depends on the geometric properties of the wave-vector space.

A set of modes is introduced to classify states by Lorentz-invariant mass.

Abstract

The concept of Lorenz invariant mass and mean propagation velocity have been investigated in detail for various multiphoton wave-packet states of light. Based on photodetection theory and straightforward kinematics, we presented a physically reasonable and at the same time rigorous proof that mean propagation velocity is consistent with the Lorentz-invariant mass concept for an arbitrary multiphoton wave-packet state. We argued that mean propagation velocity is less than the speed of light constant in vacuum and is governed by geometric properties of state's amplitude in wave-vector space for arbitrary wave-packet states. To classify states with different fixed values of Lorentz-invariant mass, we introduced a specific set of modes that allow us to describe the wave-packet state in its rest frame.