Quantum mechanics on a space-time lattice using path integrals in a minkowski metric

A simple model of many-body quantum mechanics governed by completely local interactions in ordinary three-dimensional space is presented. The equations of motion, involving no Euclideanization of time, are elementary extensions of those describing random walks on a square lattice, and are far simpler than those obtained through standard path-integral theory. A quantity is defined in terms of populations of particles on the lattice, whose expectation value is proportional to the square of the multiparticle wave functions associated with the system; for sufficiently microscopic measurement scales, this generalized density may take on negative values, thereby circumventing the constraints imposed by Bell's inequality.