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

Romeo Brunetti, Klaus Fredenhagen, Pedro Lauridsen Ribeiro
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.

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