Higher derivative extensions of 3d Chern–Simons models: conservation laws and stability

Kaparulin, D. S.; Karataeva, I. Yu.; Lyakhovich, S. L.

doi:10.1140/epjc/s10052-015-3790-1

Cited by 29 publications

(72 citation statements)

References 27 publications

(91 reference statements)

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“…As it is noticed in [22], the stable higher-derivative extensions of the Chern-Simons model realize the reducible representations which are decomposed into the unitary irreps in some cases. In the other cases, the representations are non-unitary or non-decomposable.…”

Section: Introductionmentioning

confidence: 92%

“…The conservation law makes the theory stable at classical level irrespectively to interpretation of the conserved quantity. Also notice that all the considered examples [19,22] of stable higher-derivative models admit the interactions such that do not spoil classical stability. Further examples of stable interactions can be found in [23][24][25] for various higher-derivative models.…”

Section: Introductionmentioning

confidence: 93%

“…This redefinition does not affect the brackets between gauge-invariant observables, while it can alter the brackets of non-gauge-invariant quantities. The bracket (22) involves the ambiguous terms of this type, and it is the ambiguity which is controlled by the accessory parameter γ .…”

Section: Multi-hamiltonian Formulationmentioning

confidence: 99%

“…In Ref. [22], this class is further generalized, and it covers also extended Maxwell-Chern-Simons models. In all the examples of higher-derivative models considered in [19,22], the conserved tensor with bounded 00-component turns out connected with the space-time translations by a non-canonical Lagrange anchor.…”

Section: Introductionmentioning

confidence: 99%

“…We also relate the existence of bounded conserved tensors with the structure of the corresponding Poincaré group representation. In doing that, we mostly follow the general prescriptions of [22] and [51]. The section is self-contained, however.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Hamiltonian formulations and stability of higher-derivative extensions of 3d Chern–Simons

Abakumova¹,

Kaparulin²,

Lyakhovich³

2018

Eur. Phys. J. C

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Most general third-order 3d linear gauge vector field theory is considered. The field equations involve, besides the mass, two dimensionless constant parameters. The theory admits two-parameter series of conserved tensors with the canonical energy-momentum being a particular representative of the series. For a certain range of the model parameters, the series of conserved tensors include bounded quantities. This makes the dynamics classically stable, though the canonical energy is unbounded in all the instances. The free third-order equations are shown to admit constrained multi-Hamiltonian form with the 00-components of conserved tensors playing the roles of corresponding Hamiltonians. The series of Hamiltonians includes the canonical Ostrogradski's one, which is unbounded. The Hamiltonian formulations with different Hamiltonians are not connected by canonical transformations. This means, the theory admits inequivalent quantizations at the free level. Covariant interactions are included with spinor fields such that the higher-derivative dynamics remains stable at interacting level if the bounded conserved quantity exists in the free theory. In the first-order formalism, the interacting theory remains Hamiltonian and therefore it admits quantization, though the vertices are not necessarily Lagrangian in the third-order field equations.

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Section: Introductionmentioning

confidence: 92%