The foliation operator in history quantum field theory.

As a preliminary to discussing the quantization of the foliation in a history form of general relativity, we show how the discussion in an earlier work [J. Math. Phys. 43, 3053 (2002)] of a history version of free, scalar quantum field theory can be augmented in such a way as to include the quantization of the unit-length, timelike vector that determines a Lorentzian foliation of Minkowski space-time. 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 [J. Math. Phys. 43, 3053 (2002)] and (ii) considering a specific representation of the extended history algebra obtained from the multi-symplectic representation of scalar field theory. [ABSTRACT FROM AUTHOR]