  Dynamical symmetries of Born-Infeld theory can be absorbed into the spacetime
geometry, giving rise to relativistic kinematics with an additional invariant
acceleration scale. The standard Poincare group P is thereby enhanced to its
pseudo-complexified version, which is isomorphic to P x P. We construct the
irreducible representations of this group, which yields the particle spectrum
of a relativistic quantum theory that respects a maximal acceleration. It is
found that each standard relativistic particle is associated with a
`pseudo'-partner of equal spin but generically different mass. These
pseudo-partners act as Pauli-Villars regulators for the other member of the
doublet, as is found from the explicit construction of quantum field theory on
pseudo-complex spacetime. Conversely, a Pauli-Villars regularised quantum field
theory on real spacetime possesses a field phase space with integrable
pseudo-complex structure, which gives rise to a quantum field theory on
pseudo-complex spacetime.
  This equivalence between maximal acceleration kinematics, pseudo-complex
quantum field theory, and Pauli-Villars regularisation rigorously establishes a
conjecture on the regularising property of the maximal acceleration principle
in quantum field theory, by Nesterenko, Feoli, Lambiase and Scarpetta.
