V.Ya. Fainberg

How can local properties be described in field theories without strict locality

Abstract To investigate local properties of the fields that are not strictly localizable we associate a topology τO on the test function space to each space-time region O . Conditions are found which the family of topologies τO must satisfy in order that the concept of causality can be introduced into the theory. It is considered how the main properties of the Wightman functionals change when we pass to test function spaces which have less-pronounced local properties. It is shown, in particular, that the fields with exponential momentum-space growth like exp(l‖p‖) are localizable only in space-time regions large in comparison with l. This happens because not any domain in the space of several complex variables is a domain of holomorphy. A simple method for deriving Ruelles cluster property is proposed, which is applicable to nonlocalizable fields as well as to localizable ones. Making use of this property, we prove polynomial energy boundedness of the elastic scattering amplitude in nonlocalizable theories.

Local supersymmetry and Dirac particle propagator as a path integral

Abstract Proceeding from the reparametrization-invariant and locally supersymmetric action for the Dirac particle, the path integral representation for the Green function, satisfying the first order equation in the external Maxwell field, is obtained.

A propagator for the fermionic string

Abstract Proceeding from the path integral for the open fermionic string the expression for the propagator is obtained. The result is compared with that of operator calculations for the Green function of the fermionic string. In the case of pointlike boundary conditions the expression for the propagator can be written in the form of a Kallen-Lehmann representation with increasing spectral density.

Causality, localizability, and holomorphically convex hulls

AbstractA generalization of local commutativity to the fields with an exponential momentum-space growth ∼el‖p‖ is considered. To study the local properties of such fields we associate to each space-time region

Asymptotic estimates in perturbation theory and complex instantons

\mathcal{O}

Topological Unitarity Identities in the Theory of Scalar Charged Particles Interacting Through a Pure C-S Gauge Field

a topology τ(

Chern-Simons theory of scalar particles and the Aharonov-Bohm effect (Physics Letters A 207 (1995) 1)

\mathcal{O}