  This paper describes the effects of a complex scalar scaling field on quantum
mechanics. The field origin is an extension of the gauge freedom for basis
choice in gauge theories to the underlying scalar field. The extension is based
on the idea that the value of a number at one space time point does not
determine the value at another point. This, combined with the description of
mathematical systems as structures of different types, results in the presence
of separate number fields and vector spaces, both as structures, at different
space time locations. Complex number structures and vector spaces at each
location, are scaled by a complex space time dependent scaling factor. The
effect of this scaling factor on several physical and geometric quantities has
been described in other work. Here the emphasis is on quantum mechanics of one
and two particles, their states and properties. Multiparticle states are also
briefly described. The effect shows as a complex, nonunitary, scalar field
connection on a fiber bundle description of nonrelativistic quantum mechanics.
The lack of physical evidence for the presence of this field so far means that
the coupling constant of this field to fermions is very small. It also means
that the gradient of the field must be very small in a local region of
cosmological space and time. Outside this region there are no restrictions on
the field gradient.
