We show that the relativistic analogue of the two types of time translation in a non-relativistic history theory is the existence of two distinct Poincar\'{ e} groups. The `internal' Poincar\'{ e} group is analogous to the one that arises in the standard canonical quantisation scheme; the `external' Poincar\'{ e} group is similar to the group that arises in a Lagrangian description of the standard theory. In particular, it performs explicit changes of the spacetime foliation that is implicitly assumed in standard canonical field theory.
Categories: gr-qc math-ph math.MP quant-ph