Waves transverse standing equation

Whittaker s early work [27,28] is the precursor [4] to twistor theory and is well developed. Whittaker showed that a scalar potential satisfying the Laplace and d Alembert equations is structured in the vacuum, and can be expanded in terms of plane waves. This means that in the vacuum, there are both propagating and standing waves, and electromagnetic waves are not necessarily transverse. In this section, a straightforward application of Whittaker s work is reviewed, leading to the feasibility of interferometry between scalar potentials in the vacuum, and to a trouble-free method of canonical quantization. 

In general, each vector equation stands for six equations, one for each component of E and H in the three coordinates, but the number can be reduced by proper choice of the coordinate system. In setting all (j)j equal in the above equations we tacitly imply the validity of the reflection law. As in the discussion of the Fresnel equations we solve the problem for two orthogonal, linearly polarized waves. Other states of polarization may be represented by superposition of these solutions. For the transverse E wave (TE) the electric vector is perpendicular to the plane of incidence, and only the z-component of E exists, = E . The same is true for the transverse H wave (TM), where only the = H component is present. 

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