The breaking of space-time symmetries and the non-conservation of the associated Noether charges constitutes a central artifact in lattice field theory. In prior work we have shown how to overcome this limitation for classical actions describing point particle motion, using the world-line formalism of general relativity. The key is to treat coordinate maps (from an abstract parameter space into space-time) as dynamical and dependent degrees of freedom, which remain continuous after discretization of the underlying parameter space. Here we present latest results where we construct a reparameterization invariant classical action for scalar fields, which features dynamical coordinate maps. We highlight the following achievements of our approach: 1) global space-time symmetries remain intact after discretization and the associated Noether charges remain exactly preserved 2) coordinate maps adapt to the dynamics of the scalar field leading to adaptive grid resolution guided by the symmetries.

翻译：时空对称性的破缺及相关诺特荷的不守恒构成了晶格场论中的核心人为效应。在先前工作中，我们已通过广义相对论的世界线形式体系，展示了如何克服点粒子运动经典作用量中的这一局限。其关键在于将坐标映射（从抽象参数空间到时空）处理为动态且依赖的自由度，这些映射在底层参数空间离散化后仍保持连续性。本文提出我们构建标量场重参数化不变经典作用量的最新成果，该作用量具有动态坐标映射特性。我们重点阐述本方法的以下成就：1）离散化后全局时空对称性保持完整，相关诺特荷严格守恒 2）坐标映射能自适应标量场动力学，形成由对称性引导的自适应网格分辨率。