  This work is based on a description of quantum reference frames that seems
more basic than others in the literature. Here a frame is based on a set of
real and of complex numbers and a space time as a 4-tuple of the real numbers.
There are many isomorphic frames as there are many isomorphic sets of real
numbers. Each frame is suitable for construction of all physical theories as
mathematical structures over the real and complex numbers. The organization of
the frames into a field of frames is based on the representations of real and
complex numbers as Cauchy operators defined on complex rational states of
finite qubit strings. The structure of the field is based on noting that the
construction of real and complex numbers as Cauchy operators in a frame can be
iterated to create new frames coming from a frame. Gauge transformations on the
rational string states greatly expand the number of quantum frames as, for each
gauge U, there is one frame coming from the original frame. Forward and
backward iteration of the construction yields a two way infinite frame field
with satisfying properties. There is no background space time and there are no
real or complex numbers for the field as a whole. Instead these are relative
concepts associated with each frame in the field. Extension to include qukit
strings for different k bases, is described as is the problem of reconciling
the frame field to the existence of just one frame with one background space
time for the observable physical universe.
