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

September 10, 2012

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.

Keywords:

relativistic classical field theory, algebraic approach, observables, hyperbolic Euler-Lagrange equations