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Reducible representations of CAR and CCR are applied to second quantizationof Dirac and Maxwell fields. The resulting field operators are indeed operatorsand not operator-valued distributions. Examples show that the formalism maylead to a finite quantum field theory.Comment: Contribution to "New ideas in quantization", XXI Workshop on  Geometric Methods in Physics, Bialowieza 2002, proceedings to be published in  J. Nonlin. Math. Phys., jnmp.cls style package included, reference [3]  update

Reducible representations of CAR and CCR with possible applications to field quantization