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I am teaching myself QFT from Peskin for next years maths course and I have two questions:

  1. What is a c-number? Is it a complex number, and if so why does it mean, $[\hat{\phi}(x),\hat{\phi}(y)]~=~<0|[\hat{\phi}(x),\hat{\phi}(y)]|0> {\bf 1}$.

  2. Is $[\hat{\phi}(x),\hat{\phi}(y)]|$ still equal to zero if $(x^{2}-y^{2})<0 $ ?

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c-number stands for classical number i.e. it is not an operator like $\hat{p}, \hat{x}$, but just the usual quantity in classical mechanics. –  ramanujan_dirac Apr 28 '13 at 6:07
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$x^2-y^2<0$ does not always belong to space/light/time like interval, so it is not obviously to say. For $(x-y)^2<0$ under +--- metric, the commutator is zero. –  user26143 Jul 18 '13 at 18:59
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