N-Galilean conformal algebras and quantum theory with higher order time derivatives

TL;DR

This paper demonstrates that the centrally extended N-Galilean conformal algebra, for odd N, is the maximal symmetry algebra of a Schrödinger equation derived from a free Lagrangian with higher-order time derivatives.

Contribution

It establishes a connection between higher-order time derivative Schrödinger equations and maximal symmetry algebras, specifically the N-Galilean conformal algebra for odd N.

Findings

Centrally extended N-Galilean conformal algebra is the maximal symmetry of the higher-derivative Schrödinger equation.

The algebra applies to free Lagrangians with (N+1)/2-th order time derivatives.

The work extends understanding of symmetries in higher-order quantum systems.

Abstract

It is shown that centrally extended N-Galilean conformal algebra, with N-odd, is the maximal symmetry algebra of the Schrodinger equation corresponding to the free Lagrangian involving (N+1)/2-th order time derivatives.