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Generalized stochastic Schroedinger equations for state vector collapse
A number of authors have proposed stochastic versions of the Schr\"odinger
equation, either as effective evolution equations for open quantum systems or
as alternative theories with an intrinsic collapse mechanism. We discuss here
two directions for 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 Schr\"odinger equations for which state vector collapse is provable.
Second, we explore the problem of formulating a relativistic stochastic
Schr\"odinger 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 , arising from the local double commutator in
the drift term.Comment: 24 pages Plain TeX. Minor changes, some new references. To appear in
Journal of Physics