Space of Quantum Theory Representations of Natural Numbers, Integers, and Rational Numbers
| dc.creator | Benioff, Paul | |
| dc.date | 2007-04-26 | |
| dc.date.accessioned | 2026-07-07T07:59:02Z | |
| dc.date.available | 2026-07-07T07:59:02Z | |
| dc.description | 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. | |
| dc.description | 32 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0704.3574 | |
| dc.identifier | http://arxiv.org/abs/0704.3574 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128224 | |
| dc.subject | Quantum Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | Space of Quantum Theory Representations of Natural Numbers, Integers, and Rational Numbers | |
| dc.type | text |