An intrinsic description of the Hamilton-Cartan formalism for first-order Berezinian variational problems determined by a submersion of supermanifolds is given. This is achieved by studying the associated higher-order graded variational problem through the Poincaré-Cartan form. Noether theorem and examples from superfield theory and supermechanics are also discussed.

We present a detailed analysis of the orbital stability of the Pais-Uhlenbeck oscillator, using Lie-Deprit series and Hamiltonian normal form theories. In particular, we explicitly describe the reduced phase space for this Hamiltonian system and give a proof for the existence of stable orbits for a certain class of self-interaction, found numerically in previous works, by using singular symplectic reduction.

We construct a family of quantum scalar fields over a p−adic spacetime which satisfy p−adic analogues of the Gårding-Wightman axioms. Most of the axioms can be formulated the same way in both, the Archimedean and non-Archimedean frameworks; however, the axioms depending on the ordering of the background field must be reformulated, reflecting the acausality of p−adic spacetime. The p−adic scalar fields satisfy certain p−adic Klein-Gordon pseudodifferential equations. The second quantization of the solutions of these Klein-Gordon equations corresponds exactly to the scalar fields introduced here.

Abstract. We study the determination of the second-order normal form for perturbed Hamiltonians2 H 2 , relative to the periodic flow of the unperturbed Hamiltonian H 0 . The formalism presented here is global, and can be easily implemented in any CAS. We illustrate it by means of two examples: the Hénon-Heiles and the elastic pendulum Hamiltonians.