On Relativistic Irreducible Quantum Fields Fulfilling CCR
POWERS  has shown that in more than one space dimension all irreducible Fermi fields which fulfill CAR are necessarily free fields. Based on estimates given by HERBST  we shall show that irreducible Bose fields which fulfill CCR are free fields in d > 3 space dimensions. In d = 3 and d = 2 space dimensions CCR restricts the interaction to be renormalizable. The superrenormalizable models do fulfill CCR as we know from Constructive Quantum Field Theory.
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