  A model is discussed where all operators are constructed from a quantum
scalar field whose energy spectrum takes on all real values. The Schr\"odinger
picture wave function depends upon space and time coordinates for each
particle, as well as an inexorably increasing evolution parameter $s$ which
labels a foliation of space-like hypersurfaces. The model is constructed to be
manifestly Lorentz invariant in the interaction picture. Free particle states
and interactions are discussed in this framework. Then, the formalism of the
CSL (Continuous Spontaneous Localization) theory of dynamical collapse is
applied. The collapse-generating operator is chosen to to be the particle
number space-time density. Unlike previous relativistically invariant models,
the vacuum state is not excited. The collapse dynamics depends upon two
parameters, a parameter $\Lambda$ which represents the collapse rate/volume and
a scale factor $\ell$. A common example of collapse dynamics, involving a clump
of matter in a superposition of two locations, is analyzed. The collapse rate
is shown to be identical to that of non-relativistic CSL when the GRW-CSL
choice of $\ell=a=10^{-5}$cm, is made, along with $\Lambda=\lambda/a^{3}$
(GRW-CSL choice $\lambda=10^{-16}s^{-1}$). However, it is also shown that the
change of mass of a nucleon over the age of the universe is then unacceptably
large. The case where $\ell$ is the size of the universe is then considered. It
is shown that the collapse behavior is satisfactory and the change of mass over
the age of the universe is acceptably small, when $\Lambda= \lambda/\ell
a^{2}$.
