# The energy-momentum conservation law in two-particle system for twist-deformed Galilei Hopf algebras

## TL;DR

This paper investigates how energy and momentum are conserved in two-particle systems within twist-deformed Galilei Hopf algebras, revealing conditions for discrete energy and momentum values based on symmetrized addition laws.

## Contribution

It introduces consistent energy-momentum addition laws for two-particle systems in twist-deformed Galilei Hopf algebras, highlighting the impact of symmetrization on discretization of physical quantities.

## Key findings

- Energy-momentum addition laws are consistent with coproducts.
- Vanishing total four-momentum implies discrete energies and momenta.
- Symmetrized addition rules lead to quantized physical values.

## Abstract

In this article we discus the energy-momentum conservation principle for two-particle system in the case of canonically and Lie-algebraically twist-deformed Galilei Hopf algebra. Particularly, we provide consistent with the coproducts energy and momentum addition law as well as its symmetric with respect the exchange of particles counterpart. Besides, we show that the vanishing of total fourmomentum for two Lie-algebraically deformed kinematical models leads to the discret values of energies and momenta only in the case of the symmetrized addition rules.