Non-Localizability and Asymptotic Commutativity

Details Non-Localizability and Asymptotic Commutativity Non-Localizability and Asymptotic Commutativity

1992-11-24

arxiv.org/abs/hep-th/9211099v2

Theor.Math.Phys.93:1438-1449,1992; Teor.Mat.Fiz.93:514-528,1992

Physics

High Energy Physics

High Energy Physics - Theory

This version is identical to the initial one whose ps and pdf files were unavailable, with few corrections of misprints

Scientific paper

10.1007/BF01016400

The mathematical formalism commonly used in treating nonlocal highly singular interactions is revised. The notion of support cone is introduced which replaces that of support for nonlocalizable distributions. Such support cones are proven to exist for distributions defined on the Gelfand-Shilov spaces $S^\beta$, where $0<\beta <1$ . This result leads to a refinement of previous generalizations of the local commutativity condition to nonlocal quantum fields. For string propagators, a new derivation of a representation similar to that of K\"{a}llen-Lehmann is proposed. It is applicable to any initial and final string configurations and manifests exponential growth of spectral densities intrinsic in nonlocalizable theories.

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