Smeared and unsmeared chiral vertex operators

We prove unboundedness and boundedness of the unsmeared and smeared chiral vertex operators, respectively. We use elementary methods in bosonic Fock space, only. Possible applications to conformal two - dimensional quantum field theory, perturbation thereof, and to the perturbative construction of the sine-Gordon model by the Epstein-Glaser method are discussed. From another point of view the results of this paper can be looked at as a first step towards a Hilbert space interpretation of vertex operator algebras.Comment: 18 pages, latex, no figure

Generalized Gram–Hadamard inequality

We generalize the classical Gram determinant inequality. Our generalization follows from the boundedness of the antisymmetric tensor product operator. We use fermionic Fock space methods