Generalized stochastic Schrodinger equations for state vector collapse

A number of authors have proposed stochastic versions of the Schrodinger equation, either as effective evolution equations for open quantum systems or as alternative theories with an intrinsic collapse mechanism. Here we discuss two directions for the generalization of these equations. First, we study a general class of norm preserving stochastic evolution equations, and show that even after making several specializations there is an infinity of possible stochastic Schrodinger equations for which state vector collapse is provable. Second, we explore the problem of formulating a relativistic stochastic Schrodinger equation, using a manifestly covariant equation for a quantum field system based on the interaction picture of Tomonaga and Schwinger. The stochastic noise term in this equation can couple to any local scalar density that commutes with the interaction energy density, and leads to collapse onto spatially localized eigenstates. However, as found in a similar model by Pearle, the equation predicts an infinite rate of energy nonconservation proportional to delta (3) ((0) over right arrow), arising from the local double commutator in the drift term.