Really? I always thought that the meaning of nonlocal is "not local". If it would mean something else, then I fear I would have to agree with vanhees71 that it is a burned word that should be avoided. Because if it doesn't mean "not local", then everybody will just form his own opinions about what it should mean.martinbn said:The distance to Andromeda is not a local quantity, but why would you call it nonlocal! The oposite of local is not always nonlocal, for example it could be global.
Well, i have seen "the local structure of manifolds..., while the global structure...". And i have never seen "the local structure of manifolds..., while the nonlocal structure...".gentzen said:Really? I always thought that the meaning of nonlocal is "not local". If it would mean something else, then I fear I would have to agree with vanhees71 that it is a burned word that should be avoided. Because if it doesn't mean "non local", then everybody will just form his own opinions about what it should mean.
But this seems consistent with what I said. You don't talk about "the not local structure of manifolds" or "the part of the structure of manifolds which is not local". So "nonlocal" and "not local" seem to mean the same thing, while "global" means something different from "not local", even so it implies "not local".martinbn said:Well, i have seen "the local structure of manifolds..., while the global structure...". And i have never seen "the local structure of manifolds..., while the nonlocal structure...".
It depends about which two-point functions you are talking. Of course two-point Green's functions or proper vertex functions do not directly descibe observables. I was thinking, however, we are talking about correlation functions referring to measurable quantities like the two-point correlation function of the field intensities for two-photon measurements (see, e.g., Scully&Zubairy, Quantum Optics, Chpt. 21).A. Neumaier said:2-point functions are called correlation functions, but in general they do not directly describe measurable correlations. They are just nonlocal mathematical expressions. Only sometimes they can be interpreted in terms of measured correlations.
Independent of this, measured correlations at distinct points are still bilocal since you compute them you need to measure at two points, not only at one.
Global is a very special case of nonlocal, meaning depending on infinitely many points along a curve or a higher-dimensional submanifold.martinbn said:Well, i have seen "the local structure of manifolds..., while the global structure...". And i have never seen "the local structure of manifolds..., while the nonlocal structure...".
The special case has the same properties as the general case, hence is as bilocal as general 2-point functions. Bilocal is not local, hence nonlocal. Pure time correlations are local.vanhees71 said:It depends about which two-point functions you are talking. Of course two-point Green's functions or proper vertex functions do not directly descibe observables. I was thinking, however, we are talking about correlation functions referring to measurable quantities like the two-point correlation function of the field intensities for two-photon measurements (see, e.g., Scully&Zubairy, Quantum Optics, Chpt. 21).