  A BCS-type wave function describes the ground state of the massless Thirring
model in the chirally broken phase. The massless Thirring model with fermion
fields quantized in the chirally broken phase bosonizes to the quantum field
theory of the free massless (pseudo)scalar field (Eur. Phys. J. C20, 723
(2001)). The wave functions of the ground state of the free massless
(pseudo)scalar field are obtained from the BCS-type wave function by averaging
over quantum fluctuations of the Thirring fermion fields. We show that these
wave functions are orthogonal, normalized and non-invariant under shifts of the
massless (pseudo)scalar field. This testifies the spontaneous breaking of the
field-shift symmetry in the quantum field theory of a free massless
(pseudo)scalar field. We show that the vacuum-to-vacuum transition amplitude
calculated for the bosonized BCS-type wave functions coincides with the
generating functional of Green functions defined only by the contribution of
vibrational modes (Eur. Phys. J. C 24, 653 (2002)) . This confirms the
assumption that the bosonized BCS-type wave function is defined by the
collective zero-mode (hep-th/0212226). We argue that the obtained result is not
a counterexample to the Mermin-Wagner-Hohenberg and Coleman theorems.
