Structured light pulses and their Lorentz-invariant mass

The Lorentz-invariant mass and mean propagation speed have been found for structured light pulses in a vacuum considered as relativistic objects. We have solved the boundary problem for such widely known field configurations as Gauss, Laguerre-Gauss, Bessel-Gauss, Hermite-Gauss and Airy-Gauss. The pulses were taken as having a temporal envelope of finite duration. We discovered that Lorentz-invariant mass and mean propagation speed significantly depend on the spatial-temporal structure of pulses. We found that mean propagation speed is independent of the full energy of the pulse and is less than the speed of light.