Aaron Collavini

In physics, all dynamical equations that describe fundamental interactions are second order ordinary differential equations in the time derivatives. In the literature, this property is traced back to a result obtained by Ostrogradski in the mid 19th century, which is the technical basis of a 'no-go' theorem for higher order theories. In this work, we review the connection of symmetry properties with the order of dynamical equations, before reconsidering Ostrogradski's result. Then, we show how Ostrogradski's conclusion is reached by applying to higher order theories concepts and method that have been specifically developed for second order theories. We discuss a potential lack of consistency in this approach, to support the claim that Ostrogradski's result applies to a class of higher order theories that is nowhere representative of generic ones: we support this claim by giving an example of a higher-order Lagrangian that is asymptotically stable, but that would be unstable under Ostrogradski's criterion. We also conclude that, when considering higher order theories as fundamental, we may need to reconsider and extend the conceptual framework on which our standard treatment of second order theories is based.

This paper provides a philosophical analysis of the contemporary debate surrounding the nature of particles, as described by one of the most recent quantum theories, Quantum Field Theory. Specifically, the paper will present the formal and philosophical details underlying the discussion on the ontological and epistemological status of particles. The aim is, therefore, to offer not only a general overview for non-expert readers but also a more rigorous examination for those who wish to further explore the technical details of the mathematical formalism upon which Quantum Field Theory is based.