# The algebraic structure of general mechanics

** Speaker:** John D. Trout, Dartmouth College

** Date:** November 10, 2022

** Abstract:** Using ideas of Strocchi, Iochum & Loupias, Faddeev & Yakubovskii, and Alfsen & Shultz, we give an operational derivation of the Jordan-Banach algebra structure of the kinematics of (bounded) observables in a general theory of mechanics (classical and quantum) from a set of four axiomatic assumptions. The central tools are the duality pairing between states and observables given by expectation values, the operational association of these expectation values with measurement outcomes in experiments and polynomial rescalings of observable measuring devices. This is joint work with Shadi Ali Ahmad ‘22.