Primon Gas

Resumen del Libro

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online.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 is attributed to Bernard Julia. Consider a simple quantum Hamiltonian H having eigenstates -prangle labelled by the prime numbers p, and having energies proportional to log p. The connections between number theory and quantum field theory can be somewhat further extended into connections between topological field theory and K-theory, where, corresponding to the example above, the spectrum of a ring takes the role of the spectrum of energy eigenvalues, the prime ideals take the role of the prime numbers, the group representations take the role of integers, group characters taking the place the Dirichlet characters, and so on.