Abstract
POWERS [1] 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 [2] 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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References
R.T. Powers: Absence of Interaction as a Consequence of Good Ultraviolett Behavior in the Case of a Local Fermi Field, Commun. Math. Phys. 4, 145–156 (1967)
I.W. Herbst: On Canonical Quantum Field Theories, J. Math. Phys. 17, 1210–1221 (1976)
K. Baumann: On Relativistic Irreducible Quantum Fields Fulfilling CCR, J. Math. Phys. 28 697–704 (1987)
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© 1987 Springer-Verlag Berlin Heidelberg
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Baumann, K. (1987). On Relativistic Irreducible Quantum Fields Fulfilling CCR. In: Mitter, H., Pittner, L. (eds) Recent Developments in Mathematical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73104-4_11
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DOI: https://doi.org/10.1007/978-3-642-73104-4_11
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