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

Abstract

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 zero-zero 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.

19 pages

References in corpus (17)

• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Critical Gravity in Four Dimensions
• Classical and quantum stability of higher-derivative dynamics
• Comments on the Dynamics of the Pais-Uhlenbeck Oscillator
• Pais-Uhlenbeck Oscillator and Negative Energies
• Giving up the ghost
• An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator
• Generalised connections and higher-spin equations
• Higher derivative extensions of $3d$ Chern-Simons models: conservation laws and stability
• Remarks on quantization of Pais-Uhlenbeck oscillators
• A perturbation theory approach to the stability of the Pais-Uhlenbeck oscillator
• Stable interactions via proper deformations
• Hamiltonian structures for Pais-Uhlenbeck oscillator
• The odd-order Pais-Uhlenbeck oscillator
• On the canonical formalism of $f(R)$-type gravity using Lie derivatives
• Canonical formalism and quantization of perturbative sector of higher-derivative theories
• Energy and stability of Pais-Uhlenbeck oscillator

Cited by in corpus (13)

• Stable interactions in higher derivative field theories of derived type
• Foundations of ghost stability
• On Negative Energies, Strings, Branes, and Braneworlds: A Review of Novel Approaches
• Stable interactions between the extended Chern-Simons theory and a charged scalar field with higher derivatives: Hamiltonian formalism
• Resonance and stability of higher derivative theories of derived type
• Higher order derivatives extension of Maxwell-Chern-Simons electrodynamics in the presence of field sources and material boundaries
• Nonminimal planar electrodynamics modified by higher-derivative terms
• Conservation laws and stability of higher derivative extended Chern-Simons
• Stability in the higher derivative Abelian gauge field theory
• Stable interactions between higher derivative extended Chern-Simons and charged scalar field
• Third order extensions of $3d$ Chern-Simons interacting to gravity: Hamiltonian formalism and stability
• Generalized Yang-Mills Theory under Rotor Mechanism
• Extended Chern-Simons model for a vector multiplet