Abstract: |
We present a speculative proposal for formulating physically discretized theories using characteristic p geometries. The resulting path integral formalism for physics in characteristic p retains more symmetries than standard lattice formulations. By way of example we illustrate how this works for some bosonic, fermionic, and supersymmetric fields theories. We discuss some potential applications such as defining a physical notion of a Weil cohomology theory, geometric engineering for characteristic p and arithmetic varieties, as well as an information theoretic interpretation of our results. Time and interest permitting, we also discuss the lifting of these notions to physics over p-adic and p-adic analytic spaces, as well as the consequences of letting the choice of prime p vary. Based on a working paper available at jjheckman.com/research |