Addendum to: Bose-Einstein Condensate and Spontaneous Breaking of Conformal Symmetry on Killing Horizons, J. Math. Phys. 46, 062303 (2005)

In the paper cited in the title local scalar QFT (in Weyl algebraic approach) has been constructed on degenerate semi-Riemannian manifolds S1 x Σ corresponding to the extension of Killing horizons by adding points at infinity to the geodesic forming the horizon. It has been proved that the theory admits a natural representation of PSL(2,R) in terms of *-automorphisms and this representation is unitarily implementable if referring to a certain invariant state λ. Among other results it has been proved that the theory admits a class of inequivalent algebraic (coherent) states {λζ}, with ζ ∈ L2(Σ), which break part of PSL(2,R) symmetry. These states, if restricted to suitable portions of M are invariant and extremal KMS states with respect a surviving one-parameter group symmetry. In this addendum we clarify the nature of that PSL(2,R) symmetry braking. We show that, in fact, spontaneous symmetry breaking occurs in the natural sense of algebraic quantum field theory: if ζ ≠ 0, there is no unitary representation of whole group PSL(2,R) which implements the *-automorphism representation of PSL(2,R) itself in the GNS representation of λζ .