Geometries of Maximal Acceleration

Abstract

We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in other important respects. In particular, they have different symmetry groups, which influence in a different way the search for an underlying dynamical theory.

21 pages, LaTex, no figures, notations changed, some remarks and some new references added

References in corpus (5)

• Representations of the Canonical group, (the semi-direct product of the Unitary and Weyl-Heisenberg groups), acting as a dynamical group on noncommuting extended phase space
• Pauli-Villars regularisation and Born-Infeld kinematics
• Invariant length scale in relativistic kinematics - Lessons from Dirichlet branes
• Almost product manifolds as the low energy geometry of Dirichlet branes
• On Maximal-Acceleration, Strings and the Group of Minimal Planck-Area Relativity Theory

Cited by in corpus (4)

• Deformed Special Relativity as an effective flat limit of quantum gravity
• Test Particles with Acceleration-Dependent Lagrangian
• Lagrangian and Presymplectic Particle Dynamics with Maximal Acceleration
• A Theory of Gravitation Covariant under $Sp(4,\mathbf{R})$}