2007/04/26 by Paul Benioff, Benioff, Paul
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Algorithms and Data Compression #Computability, Logic, AI Algorithms #FOS: Physical sciences #Fractal and DNA sequence analysis #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.0704.3574
openalex publication_date 2007/04/26 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
This paper extends earlier work on quantum theory representations of natural\nnumbers N, integers I, and rational numbers Ra to describe a space of these\nrepresentations and transformations on the space. The space is parameterized by\n4-tuple points in a parameter set. Each point, (k,m,h,g), labels a specific\nrepresentation of X = N, I, Ra as a Fock space FXk,m,h of states of\nfinite length strings of qukits q and a string state basis BXk,m,h,g. The\npair (m,h) locates the q string in a square integer lattice I \× I, k is\nthe q base, and the function g fixes the gauge or basis states for each q. Maps\non the parameter set induce transformations on on the representation space.\nThere are two shifts, a base change operator Wk',k, and a basis or gauge\ntransformation function Uk. The invariance of the axioms and theorems for N,\nI, and Ra under any transformation is discussed along with the dependence of\nthe properties of Wk',k on the prime factors of k' and k. This suggests that\none consider prime number q's, q2, q3, q5, etc. as elementary and the\nbase k q's as composites of the prime number q's.\n