# Conservation laws and stability of higher derivative extended Chern-Simons

## TL;DR

This paper investigates the stability of higher derivative extended Chern-Simons theories, showing that bounded conserved quantities can ensure classical and quantum stability, with stability linked to unitary Poincaré representations.

## Contribution

It introduces a general class of gauge invariant extended Chern-Simons theories with multiple conserved energy-momentum tensors and establishes stability criteria based on boundedness and unitarity.

## Key findings

- Existence of conserved energy-momentum tensors in extended Chern-Simons theories.
- Stability requires the $00$-component of the conserved tensor to be bounded.
- Unstable theories correspond to nonunitary Poincaré representations.

## Abstract

The higher derivative field theories are notorious for the stability problems both at classical and quantum level. Classical instability is connected with unboundedness of the canonical energy, while the unbounded energy spectrum leads to the quantum instability. For a wide class of higher derivative theories, including the extended Chern-Simons, other bounded conserved quantities which provide the stability can exist. The most general gauge invariant extended Chern-Simons theory of arbitrary finite order $n$ admits $(n - 1)$-parameter series of conserved energy-momentum tensors. If the $00$-component of the most general representative of this series is bounded, the theory is stable. The stability condition requires from the free extended Chern-Simons theory to describe the unitary reducible representation of the Poincar\'e group. The unstable theory corresponds to nonunitary representation.