# Chryssomalis Chryssomalakos

## Generalized Quantum Relativistic Kinematics: a Stability Point of View

We apply Lie algebra deformation theory to the problem of
identifying
the stable form of the quantum relativistic
kinematical algebra. As a warm up, given Galileo's conception of
spacetime as input, some modest computer code we wrote
zeroes in on the Poincare-plus-Heisenberg algebra in
about a minute. Further ahead, along the same path,
lies a
three dimensional deformation space, with an instability
double cone through its origin. We give physical as well as
geometrical arguments supporting our view that moment, rather
than position operators, should enter as generators in the Lie
algebra. With this identification, the deformation parameters
give rise to invariant length and mass scales. Moreover, standard
quantum relativistic kinematics of massive, spinless
particles corresponds to non-commuting moment operators, a
purely quantum effect that bears no relation to spacetime
non-commutativity, in sharp contrast to earlier interpretations.