Pauli-Villars regularisation and Born-Infeld kinematics
  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. 
Frederic P. Schuller, Mattias N.R. Wohlfarth (DAMTP, Cambridge), and   Thomas W. Grimm (Hamburg)