Algebraic structure of classical field theory: kinematics and linearized dynamics for real scalar fields

DOI10.1007/S00220-019-03454-ZzbMATH Open1440.70014arXiv1209.2148OpenAlexW3106463054WikidataQ127914524 ScholiaQ127914524MaRDI QIDQ2415337

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Publication date: 21 May 2019

Published in: (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1209.2148

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