The breaking of space-time symmetries and the non-conservation of the associated Noether
charges constitutes a central artifact in lattice field theory. In [1, 2] 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 [3] 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.