  We prove that the massless neutral $\lambda\Phi^4$-theory does not possess a
unique vacuum. Based on the Wightman axioms the non-existence of a state which
preserves Poincar{\'e} and scale invariance is demonstrated non-perturbatively
for a non-vanishing self-interaction. We conclude that it is necessary to break
the scale invariance in order to define a vacuum state. The renormalized vacuum
expectation value of the energy-momentum tensor is derived from the two-point
Wightman function employing the point-splitting technique and its relation to
the phionic and the scalar condensate is addressed. Possible implications to
other self-interacting field theories and to different approaches in quantum
field theory are pointed out. PACS: 11.10.Cd, 11.15.Tk, 11.30.Qc
