Blair A.D. Path integrals on ultrametric spaces

Massachusetts: MIT, 1994. — 52 p.A framework for the study of path integrals on adèlic spaces is developed, and it is shown that a family of path space measures on the localizations of an algebraic number field may, under certain conditions, be combined to form a global path space measure on its adèle ring. An operator on the field of p-adic numbers analogous to the harmonic oscillator operator is then analyzed, and used to construct an Ornstein-Uhlenbeck type process on the adèle ring of the rationale.Submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology May 1994