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.
open access link
@article{Brunetti:2012ar, author = "Brunetti, Romeo and Fredenhagen, Klaus and Lauridsen Ribeiro, Pedro", title = "{Algebraic Structure of Classical Field Theory I: Kinematics and Linearized Dynamics for Real Scalar Fields}", year = "2012", eprint = "1209.2148", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1209.2148;%%" }

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