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A variational framework for higher order perturbations

Federico Chiaffredo

https://orcid.org/0009-0004-7316-3879

Dipartimento di Matematica, University of Torino, Via C. Alberto 10, 10123 Torino, Italy

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Lorenzo Fatibene

https://orcid.org/0000-0003-3159-1272

Dipartimento di Matematica, University of Torino, Via C. Alberto 10, 10123 Torino, Italy

Istituto Nazionale di Fisica Nucleare, University of Torino, Via P. Giuria 1, 10125 Torino, Italy

E-mail Address: lorenzo.fatibene@unito.it

Corresponding author.

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Marco Ferraris

https://orcid.org/0000-0002-8899-2969

Dipartimento di Matematica, University of Torino, Via C. Alberto 10, 10123 Torino, Italy

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Emanuele Ricossa

https://orcid.org/0009-0009-2606-3425

Dipartimento di Matematica, University of Torino, Via C. Alberto 10, 10123 Torino, Italy

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, and

Davide Usseglio

https://orcid.org/0000-0003-2427-9547

Scuola Superiore Meridionale, Largo San Marcellino 10, 80138 Naples, Italy

Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126 Naples, Italy

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https://doi.org/10.1142/S0219887824400073Cited by:1 (Source: Crossref)

This article is part of the issue:

20th Anniversary Special Issue — From Quantum Information to Cosmology: Exploring the Frontiers of Geometric Methods in Physics

Abstract

A covariant, global, variational framework for perturbations in field theories is presented. Perturbations are obtained as vertical vector fields on the configuration bundle and they drag, exactly, solution into solutions.

The flow of a perturbation drags solutions into solutions and the dragged perturbed solutions can be expanded in a series with respect to the flow parameter, hence it contains perturbations at any order.

Mechanics is included as a special case. As a simple application, we recover the well-known discussion about stability of geodesics on a sphere $S_{2}$ .

Keywords:

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