Editing Möbius function (section)

===Physics===
The Möbius function also arises in the [[primon gas]] or [[free Riemann gas]] model of [[supersymmetry]]. In this theory, the fundamental particles or "primons" have energies <math>\log(p)</math>. Under [[second quantization]], multiparticle excitations are considered; these are given by <math>\log(n)</math> for any natural number <math>n</math>. This follows from the fact that the factorization of the natural numbers into primes is unique.

In the free Riemann gas, any natural number can occur, if the [[primon gas|primons]] are taken as [[boson]]s. If they are taken as [[fermion]]s, then the [[Pauli exclusion principle]] excludes squares. The operator 
[[(-1)^F|<math>(-1)^F</math>]] that distinguishes fermions and bosons is then none other than the Möbius function <math>\mu(n)</math>.

The free Riemann gas has a number of other interesting connections to number theory, including the fact that the [[partition function (statistical mechanics)|partition function]] is the [[Riemann zeta function]]. This idea underlies [[Alain Connes]]'s attempted proof of the [[Riemann hypothesis]].{{sfn|Bost|Connes|1995|pp=411–457}}