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

Brunetti, Romeo; Fredenhagen, Klaus; Lauridsen Ribeiro, Pedro

doi:10.1007/s00220-019-03454-z

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

Sep, 2012

66 pages

Published in:

Commun.Math.Phys. 368 (2019) 2, 519-584

Published: May 4, 2019

e-Print:

1209.2148 [math-ph]

DOI:

10.1007/s00220-019-03454-z (publication)

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Abstract: (arXiv)

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 focuses mainly on the observables over field configurations, given by certain spaces of functionals which are studied here in depth. The analysis of such functionals is characterized by a combination of geometric, analytic and algebraic elements which (1) make our approach 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 their linearizations.

Note:

68 pages, no figures. Version 7: very minor corrections, DOI added. Version published (Online First) in Communications in Mathematical Physics, journal reference will be added when available

relativistic classical field theory
algebraic approach
observables
hyperbolic Euler-Lagrange equations
Nash-Moser-Hoermander theorem
field theory: classical
field theory: algebra
field theory: scalar
differential equations
kinematics

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