A dynamical system is called localizable if its wave functions can be expressed in terms of variables, each referring to physical conditions at only one point in space-time. These variables may be at points on any three-dimensional space-like surface in space-time.A general investigation is made of how the wave function varies when the surface is varied in any way. The variation of the wave function is given by equations of the Schr\"odinger type involving certain operators ${H}^{n}(u)$ which play the role of Hamiltonians. The commutation relations for these operators are obtained (Eqs. (50), (51)). The theory works entirely with relativistic concepts and it provides the general pattern which any relativistic quantum theory must conform to, provided the dynamical system is localizable.