Evolution time Klein-Gordon equation and derivation of its nonlinear counterpart

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Abstract
Recently, relativistic quantum mechanical wave equations involving an extra scalar evolution parameter (analogous to proper time) have been increasingly studied in the literature. Since the physical meaning of this parameter is still very much a matter of discussion the authors aim to give it a clear physical meaning and then to proceed to a stochastic derivation of a nonlinear evolution time Klein-Gordon equation with a view to representing possible vacuum dissipative effects.