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

## TL;DR

This paper develops a Hamiltonian formalism for the extended Chern-Simons theory with higher derivatives, identifying conserved tensors and stable interactions with charged scalar fields, and explores multiple Hamiltonian formulations including Ostrogradski's.

## Contribution

It introduces a multi-Hamiltonian framework for higher-derivative extended Chern-Simons theory, including stable interactions and multiple non-canonically related Hamiltonian formulations.

## Key findings

- Existence of a series of conserved tensors with Hamiltonian components.
- Multiple Hamiltonian formulations including Ostrogradski's.
- Stable interactions with charged scalar fields preserving specific Hamiltonians.

## 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.