  As a preliminary to discussing the quantisation of the foliation in a history
form of general relativity, we show how the discussion in \cite{SavQFT1} of a
history version of free, scalar quantum field theory can be augmented in such a
way as to include the quantisation of the unit-length, time-like vector that
determines a Lorentzian foliation of Minkowski spacetime. We employ a Hilbert
bundle construction that is motivated by: (i) discussing the role of the
external Lorentz group in the existing history quantum field theory
\cite{SavQFT1}; and (ii) considering a specific representation of the extended
history algebra obtained from the multi-symplectic representation of scalar
field theory.
