Renormalized products of the generalized free field and its derivatives

Abel Klein

Vol. 45 (1973), No. 1, 275–292

DOI: 10.2140/pjm.1973.45.275

Abstract

Renormalized products of the generalized free field and its derivatives are shown to exist as continuous sesquilinear forms on the C^∞-vectors of the adjusted free Hamiltonian. Smeared in space and time, with some restrictions on the time smearing, and mild restrictions on the generalized free field, they are shown to be densely defined operators, admitting a self-adjoint extension when the smearing is even in time. Lorentz covariance of these products is shown.

Mathematical Subject Classification

Primary: 81.47

Milestones

Received: 12 November 1971

Published: 1 March 1973