Natural number dynamics: Reconstructing physics from generalised atomicity

A novel approach is presented in which some key basic equationsof physics are reconstructed from a generalized atomicity viewpointi.e., one in which a system is characterised simply by the number ofitems it contains and hence by the natural numbers alone. The naturalnumbers may then be associated with the eigenvalue spectrum of anoperator. The non-negative nature of the natural numbers leads tothe properties of creation and annihilation operators. By examiningthe parastatistical properties of the number operator, it is also shownthat there is only one linear representation that allows a primitivesystem to be created. An interpretation of the nonlinear factorizationof the number operator is also given in terms of the Hamiltonian forbound states of the Schr ̈odinger equation for the case of general one-dimensional potentials. Introducing multiple categories of items yieldsthe standard equations of many-body systems with interaction andscattering, and the existence of bosons and fermions.