Primon

In mathematical physics, the primon gas or free Riemann gas is a toy model illustrating in a simple way some correspondences between number theory and ideas in quantum field theory and dynamical systems. It is a quantum field theory of a set of non-interacting particles, the primons; it is called a gas or a free model because the particles are non-interacting. The idea of the primon gas was independently discovered by Donald Spector and Bernard Julia. Later works by Bakas and Bowick and Spector explored the connection of such systems to string theory.

Consider a space with states eigenstates ${\displaystyle |p\rangle }$ labelled by the prime numbers p. The second-quantized converts states into particles, the primons. A multi-particle state is given by the numbers ${\displaystyle k_{p}}$ of primons in the single-particle states ${\displaystyle p}$:

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