No-Go Theorem for Quasiparticle BEC in the Spin-Boson Model

We analyze the possibility of Bose-Einstein condensation (BEC) at finite temperature in the spin-boson model within the frameworks of functional integral representations and the resolvent algebra. Because a sesquilinear form arising from the zero mode appears, analogous to the case of the free Bose gas, a BEC-type component is also formally present in the spin-boson model. However, according to arxiv:1207.4621, quasiparticles do not undergo BEC, so we have to exclude this possibility. A no-go theorem for BEC is obtained, but we find that the spin-boson model is not a model that follows the criterion in arxiv:1207.4621.