Continuum limit for a discrete Hodge–Dirac operator on square lattices

We study the continuum limit for Dirac–Hodge operators defined on n dimensional square lattice $$h\mathbb {Z}^n$$ as h goes to 0. This result extends a first order discrete differential operator known convergence of Schrödinger their continuous counterpart. To be able define such analog, we start by defining an alternative framework higher–dimensional calculus. believe that this framework, generalize standard one simplicial complexes, could independent interest. then express our acting forms finally show operator.