Abstract Details
Abstracts
Author: Alexander S. Glasser
Requested Type: Pre-Selected Invited
Submitted: 2019-02-22 12:44:36
Co-authors: Hong Qin
Contact Info:
Princeton University
100 Stellarator Rd
Princeton, NJ 08540
USA
Abstract Text:
While conservation laws are a mainstay of fundamental physics, their status in discrete simulations has been rather more elusive. Because the discrete spacetimes of computer simulations break Poincaré invariance, conservation of energy-momentum has historically proven especially difficult. In two recent papers [1,2], however, a first-principles algorithm was discovered that exactly conserves all ten energy-momenta of the Poincaré group for a discrete lattice field theory called ‘5-vector theory’. While closely resembling a scalar field, 5-vector theory redefines the Poincaré symmetries so that they act in the manner of a gauge field--not on the ‘horizontal’ spacetime manifold, but on ‘vertical’ dynamical fields, including the 5-vector itself. This so-called ‘Poincaré lift’ unburdens spacetime, affording its lattice discretization without sacrificing 5-vector theory’s Poincaré invariance. In the present work, we sharpen our understanding of the relationship between the Poincaré gauge symmetries of 5-vector theory’s discrete action and its exact conservation laws. In the formalism of Noether’s Second Theorem, we study the derivation of conservation laws from the local symmetries of gauge-symmetric discrete actions. By extending the matter and gauge fields of 5-vector theory, we further explore the utility of the Poincaré lift in defining algorithms for plasma simulations that conserve energy, momentum and charge, and we reflect upon the gauge symmetries of existing plasma simulation algorithms.
[1] A.S. Glasser and H. Qin, arXiv:1902.04395 (2019).
[2] A.S. Glasser and H. Qin, arXiv:1902.04396 (2019).
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