p-Adic Dirac Equations, Continuous-Time Quantum Walks, and Quantum Networks
We introduce a new class of p-adic Dirac equations, formulated in the standard axiomatic framework of quantum mechanics, in which the ordinary spatial derivatives are replaced by non-local operators built from arbitrary integrable kernels. We diagonalize the resulting free Dirac Hamiltonian in momentum space, construct its plane-wave solutions, determine its spectrum, and establish a p-adic charge-conjugation symmetry relating particle and antip...
