Extension of the Chern–Simons Theory: Conservation Laws, Lagrange Structures, and Stability

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

doi:10.1007/s11182-017-0997-7

Cited by 2 publications

(5 citation statements)

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“…This connection can be traced by the Lagrange anchor method along the same lines as in the paper [51]. From this perspective, any representative of the series (9) satisfying condition (12) can be viewed as energy-momentum.…”

Section: Conserved Tensorsmentioning

confidence: 98%

“…In Ref. [51], it has been found that the model admits multiple conserved tensors being connected with the time translation by the Lagrange anchors. The anchors are polynomials in the Chern-Simons operator * d. The set of conserved quantities can include bounded ones.…”

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%

“…Depending on the values of the parameters, the action (1) can reproduce various 3d field theories, including the Chern-Simons-Proca theory [45], [46], topologically massive gauge theory [47], [48], Maxwell-Chern-Simons-Proca model [49], [50], Lee-Wick electrodynamics [3], [4] and extended Chern-Simons [5]. The classical stability of the model ( 1) is considered in the works [22], [51]. It has been found that the model admits multiple conserved tensors being connected with the time translation by the Lagrange anchors.…”

Section: Introductionmentioning

confidence: 99%

“…Here, z is considered as a formal complex-valued variable, and α k are the parameters of the model (1). As is established in [51], the model (1) admits a bounded conserved tensor and, hence, it is stable iff all the non-zero simple roots of equation ( 2) are real, while zero root may have the maximal multiplicity 2, and no roots occur with a higher multiplicity.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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: Conserved Tensorsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%