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I thought light like singularity is where the geodesics end on a lightlike hypersurface and can't be extended anymore. I guess its different than light cone singularity. Lot's of places have mention of it, but I wanted to know its definition for sure.

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You may have encountered it in a different context, but I recognize it from the topic of singularities of correlation functions in quantum field theory. In massless field theories such correlation fucntions becomes singular for points which are lightlike separated, and the structure of such singularities is determined by good physical principles such as locality and unitarity.

Then again, I may be completely off the mark. In any event, except for the linguistic similarity, I don't think it has to do with null singularities in spacetime.

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Thanks a lot Moshe! I have indeed seen it in the context of QFT correlators. So, let me rephrase..whenever the point of operator insertions are light like separated, the singularity is light cone singularity. Why is the name light cone (I know about l.c coord.)? May be I should read it from some place first. Can you please also suggest me some QFT references (not too old preferably) where it has been discussed (specially emphasizing its connection with locality unitarity etc)? – user1349 Jan 16 '11 at 3:09
Lightcone because both points are on the lightcone of each other, in other words they are null separated. Usually the singularities are discussed in momentum space, where they arise when some internal state goes on-shell (which means, for massless particles, the momentum becomes null). The issue of singularities of correlation functions is old and extensive (look at the first chapter of "The Analytic S-Matrix", it is old but good exposition, I think Weinberg's QFT book also has a good discussion). – user566 Jan 16 '11 at 3:18
Also, light cone here is a slight abuse of language, it really refers to the boundary of the light cone, people are not always pedantic about using precise language. – user566 Jan 16 '11 at 3:24
Another thing that comes to mind: it seems to me the term is mostly used by relativists, in the context of QFT in curved space, where propagators becomes singular when they are null separated (in the curved metric). Maybe because in this context you tend to work in position space, whereas in ordinary QFT it is easiest to work in momentum space. – user566 Jan 16 '11 at 3:28
Dear Moshe, concerning your remark that it is abusing language, well, it depends. In topology, cone is anything that connects a point with a base. If the base is a circle, the corresponding cone is just the surface of what you call the cone. ;-) But even if you proved that the "solid cone" is the only accurate interpretation of "cone" in the geometry, it would still be an OK name because, while the correlator goes singular only on the boundary, it is getting really big already inside the solid cone :-) and it is strictly zero outside the solid cone, by causality. – Luboš Motl Jan 16 '11 at 9:18

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