将数分解为素数看作是粒子衰变为基本粒子的能量守恒
Factorization of number into prime numbers viewed as decay of particle into elementary particles conserving energy
摘要：
数论被认为是，通过提出量子力学模型和弦状模型在零和有限的温度，其中的因数分解成素数被视为粒子衰变成基本粒子保存能量。在这些模型中，由整数$n$标记的粒子的能量被假定或导出为与$\ln n$成比例。估算了类弦模型在有限温度下的单圈真空振幅、自由能和配分函数，并与zeta函数进行了比较。在相互作用开启后，自由能中的$SL(2, {\bf Z})$模对称性被分解为整数的加性对称性${\bf Z}_{+}$。在zeta函数后面的动力学模型中，准备了用素数标记的场。另一方面，我们模型中的字段不是用素数而是用整数来标记的。然而，我们可以通过衰变率来理解一个数是质数还是非质数，即通过相应的粒子通过守恒能量的相互作用可以衰变或不衰变。其中，超对称类弦模型的优点是零点能被取消，能级可以稳定地抵抗辐射修正。
英文摘要：
Number theory is considered, by proposing quantum mechanical models and string-like models at zero and finite temperatures, where the factorization of number into prime numbers is viewed as the decay of particle into elementary particles conserving energy. In these models, energy of a particle labeled by an integer $n$ is assumed or derived to being proportional to $\ln n$. The one-loop vacuum amplitudes, the free energies and the partition functions at finite temperature of the string-like models are estimated and compared with the zeta functions. The $SL(2, {\bf Z})$ modular symmetry, being manifest in the free energies is broken down to the additive symmetry of integers, ${\bf Z}_{+}$, after interactions are turned on. In the dynamical model existing behind the zeta function, prepared are the fields labeled by prime numbers. On the other hand the fields in our models are labeled, not by prime numbers but by integers. Nevertheless, we can understand whether a number is prime or not prime by the decay rate, namely by the corresponding particle can decay or can not decay through interactions conserving energy. Among the models proposed, the supersymmetric string-like model has the merit of that the zero point energies are cancelled and the energy levels may be stable against radiative corrections.
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