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.