De Broglie waves may be a reflection of a deformation inherent in the path algebra of phase space. This may be trivial algebraically but not when the topology is taken into account. On a Riemannian manifold equipped with a suitable closed 2-form, the product of paths, which is ordinarily their concatenation, can be deformed by multiplication by a scalar weight giving rise to a function on paths. In flat phase space the associated function is periodic with period the de Broglie wave length. (This is an update of the talk I gave in March of last year