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

TL;DR

This paper introduces a one-parameter family of energy and momentum definitions in 1+1 dimensional special relativity, maintaining key invariance and conservation properties while allowing different velocity dependencies.

Contribution

It constructs a family of additive energy-momentum definitions in 1+1D STR that preserve Lorentz invariance and conservation, revealing no further freedom under natural conditions.

Findings

Energy and momentum can be modified without losing invariance or conservation.

The family parameter determines whether energy and momentum grow faster or slower with velocity.

The modified definitions closely match standard ones at wide velocity ranges.

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.