On fermion grading symmetry
  We consider the univalence superselection rule. One would say perhaps ``There is no indication in nature to invalidate this rule. Fermions do not condensate!'' To explain our motivation, let us recall the correspondence of fermion systems and Pauli systems by the Jordan-Wigner transformation. For a finite lattice, fermion grading symmetry corresponds to the Pauli grading. For an infinite lattice, the Pauli-grading can be spontaneously broken e.g. for the XY-model. What is the status of the fermion grading? Nature tells that fermion grading symmmetry cannot be broken for any physical model. But it seems that its rigorous support is needed. 
Hajime Moriya