The physical observer I: Absolute and relative fields

Quantum Jet Theory (QJT) is a deformation of QFT where also the quantum dynamics of the observer is taken into account. This is achieved by introducing relative fields, labelled by locations measured by rods relative to the observer's position. In the Hamiltonian formalism, the observer's momentum is modified: p_i \to p_i - P_i, where P_i is the momentum carried by the field quanta. The free scalar field, free electromagnetism and gravity are treated as examples. Standard QFT results are recovered in the limit that the observer's mass M \to \infty and its charge e \to 0. This limit is well defined except for gravity, because e = M in that case (heavy mass equals inert mass). In a companion paper we describe how QJT also leads to new observer-dependent gauge and diff anomalies, which can not be formulated within QFT proper.