  In relativistic quantum constraint mechanics the state of a physical system
is constrained to a 3-dimensional subspace of Minkowski 4-space. Fourier
transformation can be used to relate this state between constraint spaces in
4-position and 4-momentum space. It is shown that integral transforms of this
nature can be carried out using Lorentz-invariant 3-dimensional constraint
space coordinates such that a complete equivalence class of 4-space
representations can be constructed from the transform. This method is further
applied to develop a relativistic generalization of the Segal-Bargmann
transformation that leads to the representation of quantum systems in a
three-dimensional subspace of Bargmann 4-space.
