Rigid symmetries and conservation laws in non-Lagrangian field theory

2019

Symmetry

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.

Section: Lagrange Anchor and Generalization Of The Noether Theoremmentioning

confidence: 96%

Section: Symmetries Characteristics and Conserved Quantities Of Linmentioning

confidence: 99%

Conservation Laws and Stability of Field Theories of Derived Type

2019

Symmetry

“…Since Eqs. (1) are not variational, the correspondence between the symmetries and conservation laws should be understood in a generalized sense [23] and established with the help of the Lagrange anchor [24]. In the model under consideration the positive integral of motion E and the Lagrange anchor V have the form…”

Section: Nonlinear Oscillator With Higher Derivativesmentioning

confidence: 99%

On the Stability of a Nonlinear Oscillator with Higher Derivatives

Lyakhovich

2015

Russ Phys J

Self Cite

“…The matter is that the model admits a Lagrange anchor. As is known, the Lagrange anchor [25], being identified for not necessarily Lagrangian field equations, allows one to path-integral quantize the theory [25], [30], [31], and also to connect symmetries with conservation laws [26], [32].…”

Section: 2mentioning

confidence: 99%

Consistent interactions and involution

Lyakhovich

Sharapov

2013

J. High Energ. Phys.

Self Cite

Abstract. Starting from the concept of involution of field equations, a universal method is proposed for constructing consistent interactions between the fields. The method equally well applies to the Lagrangian and non-Lagrangian equations and it is explicitly covariant.No auxiliary fields are introduced. The equations may have (or have no) gauge symmetry and/or second class constraints in Hamiltonian formalism, providing the theory admits a Hamiltonian description. In every case the method identifies all the consistent interactions.