Algebraic Structure of Classical Field Theory: Kinematics and Linearized Dynamics for Real Scalar Fields

Romeo Brunetti, Klaus Fredenhagen, Pedro Lauridsen Ribeiro

Published 2012-09-10, updated 2017-11-12Version 3

We describe the elements of a novel structural approach to classical field theory, inspired by recent developments in perturbative algebraic quantum field theory. This approach is local and functorial, being characterized by a combination of geometric, analytic and algebraic elements which (1) make it closer to quantum field theory, (2) allow for a rigorous analytic refinement of many computational formulae from the functional formulation of classical field theory and (3) provide a new pathway towards understanding dynamics. Particular attention will be paid to aspects related to nonlinear hyperbolic partial differential equations and the functorial structure underlying our approach.