What are the general properties of 3-point correlation function of a spin-2 field?
And what about 4-point, 5-point correlation functions?
spin-3, spin-4 fields?
What mathematical catagory do these problems belong to? Are there any specific studies on them? (They are so widely used in science...)
Focus
Aug1-08, 03:15 PM
Never heard of correlation functions but wikipedia suggests that they are connected to stochastic processes. It might help if you explain what you mean by all this in terms of stochastic processes. Is two spin field a 3 dimensional process?
straybird
Aug1-08, 05:38 PM
A correlation function just describes how strongly are the probabilities of different quantities correlated to each other. It doesn't have to concern stochastic processes. I'm also not familiar with stochastic processes so I'm sorry I don't understand your question in the end...
Focus
Aug1-08, 07:06 PM
I'm guessing quantities refer to distributions? Then isn't a correlation function just the covariance? Stochastic processes are processes that at some time t have a distribution and this distribution varies with regards to time. For example X_t are distributed N(0,t) which is Brownian motion with some more assumptions. Never heard of spin fields or anything like that sorry, but it sounds quite interesting. You might have more luck at the physics forum parts.
straybird
Aug2-08, 08:09 PM
yes, thanks. I thought this question is a pure mathematical one. But when I searched about it, all literature I found is written by natural scientists and engineers. It made me feel strange. I thought this question is general enough to interest a mathematician. I just wonder if there's a lot of work done by mathematicians on the related field, or mathematicians are all thinking about bigger questions than this?
Focus
Aug2-08, 10:52 PM
Generally mathematicians seem to tackle more general questions. Usually proving something exists without giving any indication to how it can be worked out. For example, Levy processes are infinitely divisible, but it is almost impossible to find what the divisors are. There might be some work done in it by statisticians but I really would not know. They seem to do weird stuff.
Anyways, good luck with your search :)