Conservation laws and stability of field theories of derived type
type: Item
instance of: scholarly article
title: Conservation laws and stability of field theories of derived type
zbMATH Open document ID: 1425.70033
published in: Symmetry
publication date: 2019-11-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1907.03068
review text: Summary: We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another formally self-adjoint operator, while each isometry of space-time gives rise to the series of symmetries of action functional. If the wave operator is given by \(n\)-th-order polynomial then this series includes \(n\) independent entries, which can be explicitly constructed. The Noether theorem is then used to construct an \(n\)-parameter set of second-rank conserved tensors. The canonical energy-momentum tensor is included in the series, while the other entries define independent integrals of motion. The Lagrange anchor concept is applied to connect the general conserved tensor in the series with the original space-time translation symmetry. This result is interpreted as existence of multiple energy-momentum tensors in the class of derived systems. To study stability we seek for bounded-conserved quantities that are connected with the time translations. We observe that the derived theory is stable if its wave operator is defined by a polynomial with simple and real roots. The general constructions are illustrated by the examples of the Pais-Uhlenbeck oscillator, higher-derivative scalar field, and extended Chern-Simons theory.
Mathematics Subject Classification ID: 70H33
zbMATH DE Number: 7134116
zbMATH Keywords: Noether's theorem
zbMATH Keywords: generalized symmetry
zbMATH Keywords: energy-momentum tensor
zbMATH Keywords: Lagrange anchor
author: Dmitry S. Kaparulin
MaRDI profile type: Publication
OpenAlex ID: W3098972017
arXiv ID: 1907.03068
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Wikidata QID: Q127900278
DOI: 10.3390/SYM11050642
description: scientific article