Translation in is a symmetry of Minkowski space: it can be shown that it corresponds to a boost in "x", "t" coordinate around the origin. Any time translation in quantum mechanics is generated by the Hamiltonian operator. For a detector coupled to modes with a definite frequency in , we can treat as "time" and the boost operator is then the corresponding Hamiltonian. In Euclidean field theory, where the minus sign in front of the time in the Rindler metric is changed to a plus sign by multiplying formula_4 to the Rindler time, i.e. a Wick rotation or imaginary time, the Rindler metric is turned into a polar-coordinate-like metric. Therefore any rotations must close themselves after 2 in a Euclidean metric to avoid being singular. So