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In relativistic quantum constraint mechanics the state of a physical systemis constrained to a 3-dimensional subspace of Minkowski 4-space. Fouriertransformation can be used to relate this state between constraint spaces in4-position and 4-momentum space. It is shown that integral transforms of thisnature can be carried out using Lorentz-invariant 3-dimensional constraintspace coordinates such that a complete equivalence class of 4-spacerepresentations can be constructed from the transform. This method is furtherapplied to develop a relativistic generalization of the Segal-Bargmanntransformation that leads to the representation of quantum systems in athree-dimensional subspace of Bargmann 4-space.

Integral Transforms in Relativistic Quantum Constraint Mechanics