Analyticity in quantum field theory II. Causality and dispersion relations

Abstract

The consequences from causality in high-energy physics are studied, with particular reference to the well-known claim that a strong connection exists between causality and global analyticity of the scattering amplitudes. We demonstrate that this relation is not as tight as has been conventionally taken for granted, but depends on additional assumptions imposed on the scattering amplitudes in the unphysical as well as in the physical region; at present no experimental test of these extra assumptions can be given. Therefore we try to discard them and explore a new concept of causality, which assures the usual (covariant) cause-event structure only over macroscopic distances and allows for violations in microscopic regions. Quantum field theory with « shadow states » is examined and found to be consistent with macroscopic causality, though not necessarily leading to the so-called normal analytic scattering amplitudes.