# 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.

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