Space of Quantum Theory Representations of Natural Numbers, Integers, and Rational Numbers

@misc{citeulike:2939174, abstract = {This paper extends earlier work on quantum theory representations of natural numbers N, integers I, and rational numbers Ra to describe a space of these representations and transformations on the space. The space is parameterized by 4-tuple points in a parameter set. Each point, (k,m,h,g), labels a specific representation of X = N, I, Ra as a Fock space F^{X}\_{k,m,h} of states of finite length strings of qukits q and a string state basis B^{X}\_{k,m,h,g}. The pair (m,h) locates the q string in a square integer lattice I \times I, k is the q base, and the function g fixes the gauge or basis states for each q. Maps on the parameter set induce transformations on on the representation space. There are two shifts, a base change operator W\_{k',k}, and a basis or gauge transformation function U\_{k}. The invariance of the axioms and theorems for N, I, and Ra under any transformation is discussed along with the dependence of the properties of W\_{k',k} on the prime factors of k' and k. This suggests that one consider prime number q's, q\_{2}, q\_{3}, q\_{5}, etc. as elementary and the base k q's as composites of the prime number q's.}, author = {Benioff, Paul }, citeulike-article-id = {2939174}, eprint = {0704.3574}, keywords = {representations}, month = {Apr}, posted-at = {2008-06-28 13:58:38}, priority = {2}, title = {Space of Quantum Theory Representations of Natural Numbers, Integers, and Rational Numbers}, url = {http://arxiv.org/abs/0704.3574}, year = {2007} }

TY - ELEC ID - citeulike:2939174 L3 - citeulike-article-id:2939174 TI - Space of Quantum Theory Representations of Natural Numbers, Integers, and Rational Numbers N2 - This paper extends earlier work on quantum theory representations of natural numbers N, integers I, and rational numbers Ra to describe a space of these representations and transformations on the space. The space is parameterized by 4-tuple points in a parameter set. Each point, (k,m,h,g), labels a specific representation of X = N, I, Ra as a Fock space F^{X}_{k,m,h} of states of finite length strings of qukits q and a string state basis B^{X}_{k,m,h,g}. The pair (m,h) locates the q string in a square integer lattice I \times I, k is the q base, and the function g fixes the gauge or basis states for each q. Maps on the parameter set induce transformations on on the representation space. There are two shifts, a base change operator W_{k',k}, and a basis or gauge transformation function U_{k}. The invariance of the axioms and theorems for N, I, and Ra under any transformation is discussed along with the dependence of the properties of W_{k',k} on the prime factors of k' and k. This suggests that one consider prime number q's, q_{2}, q_{3}, q_{5}, etc. as elementary and the base k q's as composites of the prime number q's. KW - representations AU - Benioff, Paul PY - 2007/Apr/26/ UR - http://arxiv.org/abs/0704.3574 ER -