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Random Lattice Gauge Theories and Differential Forms

We provide a brief overview on the application of the exterior calculus of differential forms to the ab initio formulation of field theories on random simplicial lattices. In this framework, discrete analogues of the exterior derivative and the Hodge star operator are employed for the factorization of discrete field equations into a purely combinatorial (metric-free) part and a metric-dependent part. The Hodge star duality (isomorphism) is invoked to motivate the use of primal and dual lattices (a dual cell complex). The natural role of Whitney forms in the construction of discrete Hodge star operators is stressed.