coboldo

well, I tought that D(x-y) was equal to <0|phi(x)phi(y)|0>. So your answer makes me even more confused. Isn't my interpretation correct? If so. Take a FREE theory. Like a filed theory for bosonic spinless massive particles. A lambda4 theory... with lambda=0. Then <0|phi(x)phi(y)|0> = D(x-y) where D is the free propagator, i.e. exactly the integral above. So... this mean value is infinity? I have to stress that, I don't care about the "value" of the integral, I just would like it to be finite. And. If it is not, then what does this mean? It means that even free theories need to be "renormalized"?

Ok. Take a bosonic propagator. Or a Green function call it as you wish. Know what I mean, huh? The solution of ([] - m^2) D(x-y) = - delta(x-y). It's something like D(x-y) = integral over d^4p of exp(ip(x-y)) times 1 / (p^2 - m^2 +- i epsilon) Now. First of all, I don't want to bother about prefactors, "i" factors, signs, prescription (feynman, casual...) The point is. I have seen this expression so many times. (and actually NEVER used it, I'm not a scientist). Then suddendly I realized that... that... ...isn't it INFINITE?! Ok forget what happens on the poles. But we are talking about an integral over "p" in 4 dimensions. And, the integrated function goes like 1 / p^2 for p ---> infinity. Shouldn't it vanish faster than 1/p^5 for the integral to be convergent at infinity?! Oh, ok, there is an oscillating phase multiplying all that. Good. I hope it does the job, with positive and negative pieces cancelling each other. But I'm not really sure. Someone can help me understanding the whole story?! thnx in advance.