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This question already has an answer here:

Photons are the force carrier of the electromagnetic force. I do not see how this could result in a transfer of momentum that attracts objects together.

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marked as duplicate by ACuriousMind, Kyle Kanos, Gert, John Rennie, user36790 Nov 23 '15 at 10:18

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Actually A.Zee's book on "QFT in a nutshell" has a very nice explanation on this on chapter I.5, I will breifly sketch it (this is a very rough skeptch),

$$Z=\int DA e^{iS(A)} =e^{iW(J)}$$ where W(J) is given by, $$W(J)=-1/2 \int \int d^4xd^yJ(x)D(x-y)J(y)$$ where D(x-y) is the photon propogator and J(x) and J(y) refer to two lumps of matter Plugging in Photon propogator we get, $$W(J)=1/2 \int d^4kJ^\mu (k) \frac{1}{k^2}J_\mu (k)$$

$J^0$ is the charge density which for two lumps of positive charge is positive and hence the result has a positive sign. If one lump was positive and other was negative one of the J would be positive and the other J would be negative and we will get an overall negative sign hence showing that there is an attraction between unlike charges and repulsion between like charges.

So photons basically act like carriers of information from one source to another. Extending this analysis further to other spin particles we get,

Exchange between like charges gives following forces according to spin

Spin 0 = Attractive

Spin 1 = Repulsive(photon)

Spin 2 = Attractive

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  • $\begingroup$ I asked this from a professor at my local university a while back. I self study completely, so it was a favour on his part to meet me. He answered me in 4 words:"negative momentum, go away". With your post, now I can see why he said that, though I am making slow progress through the Zee book. $\endgroup$ – user81619 Nov 23 '15 at 0:35
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For the forces between elementary particles we have Feynman diagrams, where there exists a mediating particle for the interaction. In the simplest diagrams: for the strong it is the gluon, for the weak it is Zs and Ws and for the electromagnetic it is the photon.

Here is Bhabha scattering, where the electron and the positron ( attractive force) are first order in the expansion and of low energy:

bhabha1bhabha2

      annihilation                                  scattering

x axis the time axis.

For e-e- scattering only the second diagram exists at first order.

So the question should be how can there be attractive and repulsive forces. To really answer one would have to do the mathematics that the Feynman diagrams dictate and the result will tell us the the force is attractive.

I have found useful for intuitive understanding the analogue with boats throwing balls to each other, and transferring momentum for repulsion, and boomerangs for attraction.

repulsive

repulsive analogue

attractive

Momentum conservation directly for the repulsive, angular momentum conservation in the attractive. As all analogues it should not be stressed too much. Here we have a ball and a boomerang. It is a way to see that the boats can be "attracted" to each other.

In the Feynman diagrams the e+e- has an extra diagram to add to the calculation, and induce kinematically the attractive effect which the e-e- or e+e+ does not have.

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