  The discrete phase space and continuous time representation of relativistic
quantum mechanics is further investigated here as a continuation of paper I
[1]. The main mathematical construct used here will be that of an area-filling
Peano curve. We show that the limit of a sequence of a class of Peano curves is
a Peano circle denoted as $\bar{S}^{1}_{n}$, a circle of radius $\sqrt{2n+1}$
where $n \in \{0,1,\cdots\}$. We interpret this two-dimensional Peano circle in
our framework as a phase cell inside our two-dimensional discrete phase plane.
We postulate that a first quantized Planck oscillator, being very light, and
small beyond current experimental detection, occupies this phase cell
$\bar{S}^{1}_{n}$. The time evolution of this Peano circle sweeps out a
two-dimensional vertical cylinder analogous to the world-sheet of string
theory. Extending this to three dimensional space, we introduce a
$(2+2+2)$-dimensional phase space hyper-tori $\bar{S}^{1}_{n^1} \times
\bar{S}^{1}_{n^2} \times \bar{S}^{1}_{n^3}$ as the appropriate phase cell in
the physical dimensional discrete phase space. A geometric interpretation of
this structure in state space is given in terms of product fibre bundles. We
also study free scalar Bosons in the background $[(2+2+2)+1]$-dimensional
discrete phase space and continuous time state space using the relativistic
partial difference-differential Klein-Gordon equation. The second quantized
field quantas of this system can cohabit with the tiny Planck oscillators
inside the $\bar{S}^{1}_{n^1} \times \bar{S}^{1}_{n^2} \times
\bar{S}^{1}_{n^3}$ phase cells for eternity. Finally, a generalized free second
quantized Klein-Gordon equation in a higher $[(2+2+2)N+1]$-dimensional discrete
state space is explored. The resulting discrete phase space dimension is
compared to the significant spatial dimensions of some of the popular models of
string theory.
