Quantizing preserving Noether symmetries

Abstract

A procedure which obviates the constraint imposed by the conflict between consistent quantization and the invariance of the Hamiltonian description under nonlinear canonical transformation is proposed. This new quantization scheme preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger's equation. As an example, the quantization of the `goldfish' many-body problem extensively studied by Calogero et al. is presented.

References in corpus (2)

• Lagrangians Galore
• Using an old method of Jacobi to derive Lagrangians: a nonlinear dynamical system with variable coefficients

Cited by in corpus (2)

• Noether symmetries and the quantization of a Lienard-type nonlinear oscillator
• Faithful representations of Lie algebras and Homogeneous Spaces