  The Einstein-Schrodinger theory is extended to include spin-0 and spin-1/2
sources, and the theory is derived from a Lagrangian density which allows other
fields to be easily added. The original theory is also modified by including a
cosmological constant caused by zero-point fluctuations. This cosmological
constant which multiplies the symmetric metric is assumed to be nearly
cancelled by Schrodinger's ``bare'' cosmological constant which multiplies the
nonsymmetric fundamental tensor, such that the total ``physical'' cosmological
matches measurement. We show that the resulting Lambda-renormalized
Einstein-Schrodinger theory closely approximates ordinary Einstein-Maxwell
theory and one-particle quantum mechanics. In particular, the field equations
match the ordinary Einstein and Maxwell equations except for additional terms
which are $<10^{-16}$ of the usual terms for worst-case field strengths and
rates-of-change accessible to measurement. We also show that the theory
predicts the exact Lorentz force equation and the exact Klein-Gordon and Dirac
equations. And the theory becomes exactly Einstein-Maxwell theory and
one-particle quantum mechanics in the limit as the cosmological constant from
zero-point fluctuations goes to infinity. Lastly, we discuss the merits of our
Lagrangian density compared to the Einstein-Maxwell Lagrangian density.
