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arXiv · 2211.10679

Towards symmetric discretization schemes via weak boundary conditions

Alexander Rothkopf
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Abstract

The Szymanzik improvement program for gauge theories is most commonly implemented using forward finite difference corrections to the Wilson action. Central symmetric schemes naively applied, suffer from a doubling of degrees of freedom, identical to the well known fermion doubling phenomenon. And while adding a complex Wilson term remedies the problem for fermions, it does not easily transfer to real-valued gauge fields. In this talk I report on recent progress in formulating symmetric discretization schemes for classical actions of simple one-dimensional problems. They avoid doubling by exploiting the weak imposition of initial/boundary conditions. Inspired by recent work in the field of numerical analysis of partial differential equations, I construct a regularized summation-by-parts finite difference operator using boundary data based on affine coordinates. Application to a classical initial value problems with second order derivatives are presented.

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Alexander Rothkopf. 2022-11-19. Towards symmetric discretization schemes via weak boundary conditions. https://arxiv.org/abs/2211.10679

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