On Mandelstam's program in potential scattering: H. M. Nussenzveig, Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil

Abstract

We extend to quantized fields the phase-space formalism previously developed for one-particle relativistic quantum theory. An integral transform is derived which extends an arbitrary system of fields from real spacetime R4 to complex spacetime C4. In the case of free fields, the extension is analytic in the union J of the forward and backward tubes. The forward tube supports only the positive-frequency part of the field, and the backward tube the negative-frequency part. Observables such as the charge and energy-momentum are obtained by integrating field combinations over phase spaces, which are two-sheeted, six-dimensional submanifolds of J, bounded away from real spacetime R4. Consequently, the fields and their products are much more regular in phase space than on spacetime. Also, the particles associated with these fields are covariantly extended in space. Propagators carry positive- and negative-frequency components of the fields into the forward and backward tubes, respectively. For the Dirac field, the separation of positive and negative frequencies implies the complete absence of Zitterbewegung. It is furthermore shown that within the axiomatic framework, the interpretation of the complexified spacetime in terms of phase space survives the transition from free to interacting fields.