Natural number dynamics: reconstructing physics from generalized atomicity

A novel approach is presented in which some key basic equations of physics are reconstructed from a generalized atomicity viewpoint i.e., one in which a system is characterised simply by the number of items it contains and hence by the natural numbers alone. The natural numbers may then be associated with the eigenvalue spectrum of an operator. The non-negative nature of the natural numbers leads to the properties of creation and annihilation operators. By examining the parastatistical properties of the number operator, it is also shown that there is only one linear representation that allows a primitive system to be created. An interpretation of the nonlinear factorization of the number operator is also given in terms of the Hamiltonian for bound states of the Schrödinger equation for the case of general one-dimensional potentials. Introducing multiple categories of items yields the standard equations of many-body systems with interaction and scattering, and the existence of bosons and fermions.