Bose condensation with negative chemical potential

Abstract

There is widespread prejudice that the existence of Bose-condensed equilibrium states of infinite ideal boson gas requires chemical potential to be strictly zero. This is not true, in general. Using standard techniques of algebraic QFT only, we show that there exists eith invariant extensions T of Schwartz's space D(ℝ3) and Bose-condensed KMS states on the CCR algebra \(\mathfrak{A}\) (T) for every chemical potential μ≤0 (h=−Δ−μ, the one-particle Hamiltonian). The corresponding condensation fields are, in general, of rapid growth at infinity, with suggested physical implications.