Speaker: Prof. Alexander Karl Rothkopf (University of Stavanger, Norway)
Date: 4pm, Wednesday, Nov 8
Place: ASTC 516 (첨단관 516호)
Title: A discrete variational approach to initial value problems preserving spacetime symmetries
The conventional discretization of space-time entails a breaking of continuum symmetries and spoils the conservation of the associated Noether charges with ramifications for long time stability and accuracy of simulations.
In this work  we take first steps towards discretizing classical actions in coordinate space, while retaining continuum symmetries. Our proof-of-principle for a point particle in (1+1)d adopts the action formalism from general relativity, where both space x(\gamma) and time t(\gamma) are dependent variables of a worldline parameter \gamma. Discretizing in \gamma, leaves the values of both x and t continuous and thus the invariance under infinitesimal translations in (1+1)d remains intact. Building upon our previous work on solving initial values on the level of the system action  we show that the relativistic approach allows to compute numerically the classical trajectory of a particle under an arbitrary bounded potential, while conserving the relativistic Noether charge for time translation symmetry exactly and at its continuum value in the interior of the simulated domain.
 A. Rothkopf, J. Nordström, (arXiv:2307.04490)
 A. Rothkopf, J. Nordström, J.Comput.Phys. 477 (2023) 111942 (arXiv:2205.14028)