What does it mean to say that the propagator(adsbygoogle = window.adsbygoogle || []).push({});

[tex]G(x,x')=\int \frac{d^4p}{(2\pi)^4}\left(\frac{e^{ip(x-x')}}{p^2+M^2}\right) [/tex]

is nonlocal? Does that mean that if x and x' are space-like in separation, this expression is non-zero? If you did have something local represented by a Fourier transform f(p):

[tex]G(x,x')=\int \frac{d^4p}{(2\pi)^4}f(p)e^{ip(x-x')} [/tex]

how could you tell just from the form of f(p) that G(x,x') vanished for space-like separations?

For large M

[tex]G(x,x')=\left(\frac{1}{M^2}+\frac{\Box}{M^4}+...\right)\delta(x-x') [/tex]

becomes local because the delta function only allows influences at x=x'. That means the interaction is no longer just local, but instantaneous. Does being local mean being instantaneous, or the broader meaning: being time-like?

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# Locality in the propagator

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