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

Stabilization and radion in de Sitter brane-world

We consider the stabilization of de Sitter brane-world. The scalar field bulk-brane theory produces the non-trivial minimum of modulus potential where temporal radion is realized. The hierarchy problem (between Planck and electroweak scales) may be solved. However, the interpretation of radion is not so clear as in AdS brane-world. In particulary, the introduction of two times physics or pair-creation of bulk spaces or identification of one of spatial coordinates with imaginary time (non-zero temperature) may be required.Comment: LaTeX file 8 pages, minor changes, version to appear in MPL