Stable interactions between the extended Chern-Simons theory and a charged scalar field with higher derivatives: Hamiltonian formalism

Abstract

We consider constrained multi-Hamiltonian formulation for the extended Chern-Simons theory with higher derivatives of arbitrary finite order. The order $n$ extension of the theory admits $(n-1)$-parametric series of conserved tensors. The $00$-component of any representative of the series can be chosen as Hamiltonian. The theory admits a series of Hamiltonian formulations, including the canonical Ostrogradski formulation. The Hamiltonian formulations with different Hamiltonians are not connected by canonical transformations. Also, we demonstrate the inclusion of stable interactions with charged scalar field that preserves one specified Hamiltonian from the series.

10 pages, to appear in Russian Physics Journal

References in corpus (10)

• Classical and quantum stability of higher-derivative dynamics
• Higher Derivative Chern--Simons Extensions
• Classical and Quantum Dynamics of Higher-Derivative Systems
• Pais-Uhlenbeck Oscillator and Negative Energies
• Hamiltonian analysis of curvature-squared gravity with or without conformal invariance
• Stable interactions in higher derivative field theories of derived type
• Remarks on quantization of Pais-Uhlenbeck oscillators
• Higher derivative extensions of $3d$ Chern-Simons models: conservation laws and stability
• Multi-Hamiltonian formulations and stability of higher-derivative extensions of $3d$ Chern-Simons
• On the canonical formalism of $f(R)$-type gravity using Lie derivatives

Cited by in corpus (7)

• 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
• Nonminimal planar electrodynamics modified by higher-derivative terms
• Stability in the higher derivative Abelian gauge field theory
• Stability and consistent interactions in Podolsky's generalized electrodynamics
• Path Integral Quantization of Generalized Stueckelberg Electrodynamics: A Faddeev-Jackiw Approach