The Construction of Quantum Field Operators: Something of Interest

We draw attention to some tune problems in constructions of the quantum-field operators for spins 1/2 and 1. They are related to the existence of negative-energy and acausal solutions of relativistic wave equations. Particular attention is paid to the chiral theories, and to the method of the Lorentz boosts.Comment: 31 pages, no figures. The invited talk at the VIII International Workshop "Applied Category Theory. Graph-Operad-Logic", San Blas, Nayarit, Mexico, January 9-16, 2010, and at the 6th International Conference on the Dark Side of the Universe (DSU2010), Leon, Gto, Mexico, June 1-6, 201