Noninertial symmetry group with invariant Minkowski line element consistent with Heisenberg quantum commutation relations

TL;DR

This paper identifies a noninertial relativistic symmetry group that preserves a Minkowski line element and aligns with Heisenberg quantum relations, extending classical symmetry concepts to quantum noninertial frames.

Contribution

It determines a subgroup of automorphisms that leave a Minkowski line element invariant, introducing noninertial relativistic symmetries consistent with quantum mechanics.

Findings

Defines a noninertial symmetry group preserving Minkowski line element.

Connects quantum Heisenberg relations with noninertial relativistic transformations.

Provides classical limit as speed of light approaches infinity.

Abstract

The maximal symmetry of a quantum system with Heisenberg commutation relations is given by the projective representations of the automorphism group of the Weyl-Heisenberg algebra. The automorphism group is the central extension of the inhomogeneous symplectic group with a conformal scaling that acts on extended phase space. We determine the subgroup that also leaves invariant a degenerate orthogonal Minkowski line element. This defines noninertial relativistic symmetry transformations that have the expected classical limit as c becomes infinite.