New vistas on the Laplace-Runge-Lenz vector

Understand

Scalar, vector and tensor conserved quantities are essential tools in solving different problems in physics and complex, nonlinear differential equations in mathematics.

• In many guises they enter our understanding of nature: charge, lepton, baryon numbers conservation accompanied with constant energy, linear or angular total momenta and the conservation of energy-momentum/angular momentum tensors in field theories due to Noether theorem which is based on the translational and Lorentz symmetry of the Lagrangians.
• One of the oldest discovered conserved quantities is the Laplace-Runge-Lenz vector for the $1/r$-potential.
• Its different aspects have been discussed many times in the literature.