  In this paper we shall re-visit the well-known Schr\"odinger and Lindblad
dynamics of quantum mechanics. However, these equations may be realized as the
consequence of a more general, underlying dynamical process. In both cases we
shall see that the evolution of a quantum state $P_\psi=\varrho(0)$ has the not
so well-known pseudo-quadratic form
$\partial_t\varrho(t)=\mathbf{V}^\star\varrho(t)\mathbf{V}$ where $\mathbf{V}$
is a vector operator in a complex Minkowski space and the pseudo-adjoint
$\mathbf{V}^\star$ is induced by the Minkowski metric $\boldsymbol{\eta}$. The
interesting thing about this formalism is that its derivation has very deep
roots in a new understanding of the differential calculus of time. This
Minkowski-Hilbert representation of quantum dynamics is called the
\emph{Belavkin Formalism}; a beautiful, but not well understood theory of
mathematical physics that understands that both deterministic and stochastic
dynamics may be `unraveled' in a second-quantized Minkowski space. Working in
such a space provided the author with the means to construct a QS (quantum
stochastic) Duhamel principle and known applications to a Schr\"odinger
dynamics perturbed by a continual measurement process are considered. What is
not known, but presented here, is the role of the Lorentz transform in quantum
measurement, and the appearance of Riemannian geometry in quantum measurement
is also discussed.
