  Using the language of differential forms, the Kaluza-Klein theory in 4+1
dimensions is derived. This theory unifies electromagnetic and gravitational
interactions in four dimensions when the extra space dimension is compactified.
Without any ad-hoc assumptions about the five-dimensional metric, the theory
also contains a scalar field coupled to the other fields. By a conformal
transformation the theory is transformed from the Jordan frame to the Einstein
frame where the physical content is more manifest. Including a cosmological
constant in the five-dimensional formulation, it is seen to result in an
exponential potential for the scalar field in four dimensions. A similar
potential is also found from the Casimir energy in the compact dimension. The
resulting scalar field dynamics mimics realistic models recently proposed for
cosmological quintessence.
