Stationary States of Scalar and Vector Fields

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Abstract
In the presence of an electrostatic field (but not for a static world scalar or magnetostatic field) the stationary solutions of the quadratic relativistic wave equation for scalar particles do not form an orthonormal set. In spite of this they may in general be used to introduce normal coordinates for the quantum theory of this field. If the wave field and its canonical conjugate are expanded in terms of these stationary solutions, then the commutation laws for the amplitudes follow from the wave field commutators and the assumption of the integrability of the classical wave equation for arbitrary initial function and time derivative. Parallel considerations are applied to the vector field. An alternative method is described that involves the introduction of orthonormal functions and the construction of a "particle Hamiltonian."

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