  Studying the quadratic field theory on seven dimensional spacetime
constructed by a direct product of Calabi-Yau three-fold by a real time axis,
with phase space being the third cohomology of the Calabi-Yau three-fold, the
generators of translation along moduli directions of
  Calabi-Yau three-fold are constructed. The algebra of these generators is
derived which take a simple form in canonical coordinates. Applying the Dirac
method of quantization of second class constraint systems, we show that the
Schr\"{o}dinger equations corresponding to these generators are equivalent to
the holomorphic anomaly equations if one defines the action functional of the
quadratic field theory with a proper factor one-half.
