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A quantum theory representations of real (R) and complex (C) numbers is giventhat is based on states of single, finite strings of qukits for any base k > 1.Both unary representations and the possibility that qukits with k a primenumber are elementary and the rest composite are discussed. Cauchy sequences ofqukit string states are defined from the arithmetic properties. Therepresentations of R and C, as equivalence classes of these sequences, differfrom classical kit string state representations in two ways: the freedom ofchoice of basis states, and the fact that each quantum theory representation ispart of a mathematical structure that is itself based on the real and complexnumbers. These aspects enable the description of 3 dimensional frame fieldslabeled by different k values, different basis or gauge choices, and differentiteration stages. The reference frames in the field are based on each R and Crepresentation where each frame contains representations of all physicaltheories as mathematical structures based on the R and C representation.Approaches to integrating this with physics are described. It is observed thatR and C values of physical quantities, matrix elements, etc. which are viewedin a frame as elementary and featureless, are seen in a parent frame asequivalence classes of Cauchy sequences of qukit string states.

Reference Frame Fields based on Quantum Theory Representations of Real and Complex Numbers