自然数、整数和有理数的量子理论表示空间
Space of Quantum Theory Representations of Natural Numbers, Integers, and Rational Numbers
摘要：
本文扩展了自然数N，整数I和有理数Ra的量子理论表示的早期工作，以描述这些表示和变换的空间。该空间由参数集中的4元组点参数化。每个点（k，m，h，g）将X = N，I，Ra的特定表示标记为qukit q的有限长度串的状态的Fock空间F^{X}_{k，m，h}和串状态基B^{X}_{k，m，h，g}。对（m，h）将q弦定位在平方整数格I \times I中，k是q基，函数g固定每个q的规范或基态。参数集上的映射诱导表示空间上的变换。有两个移位，一个是基变换算子W_{k',k}，另一个是基或规范变换函数U_{k}。讨论了N、I和Ra的公理和定理在任何变换下的不变性以及W_{k',k}的性质对k'和k的素因子的依赖性。这意味着我们可以把素数q、q_{2}、q_{3}、q_{5}等看作初等数，把基数k q看作素数q的合成数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
