Milgrom has shown that the observed shape of many galaxies can be accounted for by a modification of the Newton law without the introduction of a large amount of dark matter. Bekenstein has furthermore shown that the Milgrom result can be derived from a modification of the Einstein metric. The essential idea is contained in a change in the Einstein metric that is conformal, resulting in a Newtonian limit that coincides with the expression used by Milgrom.  However, this structure has the problem that the scalar field associated with the conformal factor exhibits superluminal propagation modes, and does not account for the observed gravitational lensing.  Bekenstein and Sanders then inroduced a vector field as well (TeVeS), that seems to satisfy many of the conditions required.
 We have shown that starting with a relativistic Hamiltonian form which yields the Einstein goedesics through application of the Hamilton equations (as discussed in Misner, Thorne and Wheeler), the addition of a potential term (scalar field) in the Hamiltonian admits a transformation to an equivalent Hamiltonian with conformally modified metric.  The Milgrom result then implies a restriction on the form of the scalar field.
Furthermore, we have shown that the addition of a gauge type interaction on the level of the original Hamiltonian results, in the conformal equivalent structure, in a Kaluza Klein type effective metric.  The Bekenstein-Sanders TeVeS construction can easily be seen to be representable by such a Kaluza Klein metric, and thus the theory may be seen to be equivalent to a Hamiltonian formulation of relativity with a world scalar field and gauge type interactions.  We discuss also the normalization constraint that the effective gauge field must satisfy.