Factorization of number into prime numbers viewed as decay of particle into elementary particles conserving energy

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.Comment: 16 pages, no figure

Being Fascinated by Strings and Membranes: Is Kikkawa-Type Physics Possible at Ochanomizu?

On the occasion of the 60th birthday of Professor Keiji Kikkawa, Kikkawa-type physics performed at Ochanomizu was personally reviewed, and the generation of the metric is discussed with the condensation of the string fields.Comment: Latex file, 5pp. Contributed to the proceedings in honor of the 60th birthday of Professor Keiji Kikkaw

Application of Kawaguchi Lagrangian formulation to string theory

String-scalar duality proposed by Y. Hosotani and membrane-scalar duality by A. Sugamoto are reexamined in the context of Kawaguchi Lagrangian formulation. The characteristic feature of this formulation is the indifferent nature of fields and parameters. Therefore even the exchange of roles between fields and parameters is possible. In this manner, dualities above can be proved easily. Between Kawaguchi metrics of the dually related theories, a simple relation is found. As an example of the exchange between fermionic fields and parameters, a replacement of the role of Grassmann parameters of the 2-dimensional superspace by the 9th component of Neveu-Schwarz-Ramond (NSR) fermions is studied in superstring model. Compactification is also discussed in this model.Comment: 12 pages, minor modification, published in Phys. Lett.