COMPLEX NUMBERS, QUANTUM-MECHANICS AND THE BEGINNING OF TIME

A basic problem in quantizing a field in curved space is the decomposi tion of the classical modes in Positive and negative frequency. The de composition is equivalent to a choice of a complex structure in the sp ace of classical solutions. In our construction the real tunneling geo metries provide the link between this complex structure and analytic p roperties of the classical solutions in a riemannian section of space. This is related to the Osterwalder-Schrader approach to euclidean fie ld theory.