There's also the matter of the free Riemann Gas, whose partition function is the Riemann zeta function. GW Mackey wrote this about it in 1978: G.W. Mackey, Unitary Group Representation in Physics, Probability, and Number Theory (Benjamin, 1978). "...Our main point here is that one could have been led to the main outline of the proof of the prime number theorem by using the physical interpretation of Laplace transforms provided by statistical mechanics. In particular, the function -zeta'/zeta whose representation as a Dirichlet series (Laplace transform with discrete measure) plays a central role in the proof has a direct physical interpretation as the internal energy function." (p.300) Donald Spector, also unaware of Mackey's work, made a number of closely-related discoveries at the same time as Julia. D. Spector, "Supersymmetry and the Möbius inversion function", Communications in Mathematical Physics 127 (1990) 239. "We show that the Möbius inversion function of number theory can be interpreted as the operator (-1)F in quantum field theory...We will see in this paper that the function...has a very natural interpretation. In the proper context, it is equivalent to (-1)F, the operator that distinguishes fermionic from bosonic states and operators, with the fact that mu(n) = 0 when n is not squarefree being equivalent to the Pauli exclusion principle...One of the results we obtain is equivalent to the prime number theorem, one of the central achievements of number theory, in which the asymptotic density of prime numbers is computed." John Baez (my advisor) has this excellent article with plenty of references to more recent work: http://math.ucr.edu/home/baez/week199.html -- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike