ar X iv : h ep - t h / 93 11 12 9 v 1 2 2 N ov 1 99 3 STRINGS and CAUSALITY

One of the early concerns in quantum field theory was causality – can one ensure that measurements at spacelike separation do not interfere? General issues of this type were important in the days when little was understood about the underlying dynamics of particle interactions; the hope was to place constraints on the types of allowed dynamics and interactions on the basis of cherished tenets of kinematics. There were in fact two ways to approach the problem. First, one could take the point of view that only the results of scattering experiments had physical content; then causal behavior means that the scattered wave cannot reach the detector before the incident wave strikes the target. We might describe this as global causality, and it is obeyed by tachyon-free string theory S-matrices. However there is a second, local version of causality, which asks whether local measurements commute at spacelike separation. Local causality ensures global causality in ordinary field theory, and typically one can construct global violations from local ones, so it would seem that the two are equivalent. But in quantum field theory the local question is more fundamental, and can be resolved without solving any complicated global problem such as long-distance signal propagation. Local causality rests on the universal properties of field theory, e.g. that any manifold locally looks the same, rather than their implementation in any particular spacetime background. For instance we can be sure that an interacting scalar field propagating in a Schwarzschild geometry obeys the axioms of local field theory without having to solve for the full S-matrix of the problem. The consequences of causality in field theory are dispersion relations arising from the analyticity of correlation functions in the complex plane of the kinematical invariants. These dispersion relations reaveal themselves in terms of the analyticity properties of the correlation functions[1]. For instance the N-point correlation function of a scalar field 0|φ(x 1) · · · φ(x N)|0 =