Symplectic Integrators

The Geat4 toolkit lacks numerical integrators that preserve energy over the long course of simulations. Specifically, the g-2 physics experiment at Fermilab seeks to uncover whether a yet undiscovered force influences how the spin of the muon behaves.To do this it measures the polarization of the muon to seek new physics over thousands of revolutions in its custom accelerator ring. To replicate this in Geant4, the toolkit must track muons for 5,000 turns with near-perfect energy conservation and no drift in particle momentum.This necessitates the use of symplectic integration schemes to maintain the level of accuracy and precision required in the calculation. Hence this projects aims to implement the following symplectic methods in the toolkit: 1.) The Leapfrog Algorithm 2.) Boris Algorithm 3.)ESSRK method for non-separable Hamiltonians.