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

Abstract

We consider the class of higher derivative $3d$ vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For $n$-th order theory of this type, we provide a general receipt for constructing $n$-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.

arXiv comment14 pages, minor corrections

References in corpus (17)

• The stability of modified gravity models
• Classical and quantum stability of higher-derivative dynamics
• Lagrange structure and quantization
• Higher Derivative Chern--Simons Extensions
• Stable Self-Interacting Pais-Uhlenbeck Oscillator
• Massive, Topologically Massive, Models
• The Projective Unitary Irreducible Representations of the Poincaré Group in 1+2 Dimensions
• Consistent interactions and involution
• Rigid Symmetries and Conservation Laws in Non-Lagrangian Field Theory
• Remarks on quantization of Pais-Uhlenbeck oscillators
• Polarization Vectors, Doublet Structure and Wigner's Little Group in Planar Field Theory
• BRST analysis of general mechanical systems
• Hamiltonian structures for Pais-Uhlenbeck oscillator
• Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket
• Class of self-dual models in three dimensions
• Peierls brackets in non-Lagrangian field theory
• Free Fields for Any Spin in 1+2 Dimensions

Cited by in corpus (16)

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• Multi-Hamiltonian formulations and stability of higher-derivative extensions of $3d$ Chern-Simons
• Stable interactions via proper deformations
• The odd-order Pais-Uhlenbeck oscillator
• 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
• Conservation Laws and Stability of Field 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
• Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
• 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
• N=2 supersymmetric odd-order Pais-Uhlenbeck oscillator
• Generalized Yang-Mills Theory under Rotor Mechanism