Carroll-Schrodinger equation as the ultra-relativistic limit of the tachyon equation.

ABSTRACT: The Poincaré symmetry can be contracted in two ways to yield the Galilei symmetry and the Carroll symmetry. The well-known Schrödinger equation exhibits the Galilei symmetry and is a fundamental equation in Galilean quantum mechanics. However, the question remains: what is the quantum equation that corresponds to the Carroll symmetry? In this paper, we derive a novel equation in two dimensions, called the "Carroll-Schrödinger equation", which describes the quantum dynamics in the Carrollian framework. We also construct the so-called "Carroll-Schrödinger algebra" in two dimensions, which is a conformal extension of the centrally extended Carroll algebra with a dynamical exponent of [Formula: see text]. We demonstrate that this algebra is the symmetry algebra of the Carroll-Schrödinger field

SUBMITTER: Najafizadeh M 

PROVIDER: S-EPMC12015531 | biostudies-literature | 2025 Apr

REPOSITORIES: biostudies-literature