One-parameter family of additive energies and momenta in 1+1 dimensional STR

Abstract

The velocity dependence of energy and momentum is studied. It is shown that in the case of STR in the space-time of only one spatial dimension the standard energy and momentum definition can be naturally modified without lost of local Lorenz invariance, conservation rules and additivity for multiparticle system. One parameter family of energies and momenta is constructed and it is shown that within natural conditions there is no further freedom. Choosing proper family parameter one can obtain energy and momentum increasing with velocity faster or slower in comparison with the standard case, but almost coinciding with them in the wide velocity region.