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malawi_glenn

Science Advisor

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## Main Question or Discussion Point

Hello

I am trying to follow how one can define a correlation function of two quantum fields using Path integrals.

I have stumbled on equation 9.16 in Peskin, where they states that the functional integral can be split into:

[tex]\int D \phi(x) = \int D\phi _1 (\vec{x}) \int D \phi _2 (\vec{x} ) \int _{\substack{\phi (x_1^0, \vec{x}) = \phi _1 (\vec{x} ) \\\phi (x_2^0, \vec{x}) = \phi _2 (\vec{x} )}} D \phi (x)[/tex]

I was wondering how one can justify this break up? It is only an endpoint constraint imposed, but why do we have to integrate over the intermediate configurations?

Any additional insight or reading tips will be very welcomed! :-)

I am trying to follow how one can define a correlation function of two quantum fields using Path integrals.

I have stumbled on equation 9.16 in Peskin, where they states that the functional integral can be split into:

[tex]\int D \phi(x) = \int D\phi _1 (\vec{x}) \int D \phi _2 (\vec{x} ) \int _{\substack{\phi (x_1^0, \vec{x}) = \phi _1 (\vec{x} ) \\\phi (x_2^0, \vec{x}) = \phi _2 (\vec{x} )}} D \phi (x)[/tex]

I was wondering how one can justify this break up? It is only an endpoint constraint imposed, but why do we have to integrate over the intermediate configurations?

Any additional insight or reading tips will be very welcomed! :-)