Feynman Diagrams and Time Axis
Date: Spring 2013
I am confused by Feynman diagrams. Excluding the axes, everything makes sense. However, when I saw the time axis, I was perplexed because the arrows on the lines representing antiparticles pointed to the left, or backwards in time. I had thought that antimatter behaved exactly like common matter, except with opposite spins. Why does this happen in Feynman diagrams?
Confusion with the antiparticle apparently moving backward in time is understandable and is usually linked in that the researcher is reading in more meaning to the diagram than was originally intended.
Feynman diagrams are pictorial representations for terms in a perturbation series. The topology of the diagram matters (i.e: which lines are connected where), as well as the various momenta directions and vertex factors annotating the diagram. There is not much point in thinking of the internal lines and vertices as having a place or position in space-time.
Let us take an electron(e-) annihilating a positron(e+) to produce two photons. The electron line is shown with an arrow that goes forward in time for the e- and backwards for the e+ as if a positron is going back in time. This was an interpretation that Dr. Feynman preferred.
The central line shows the e-/e+ annihilation as if it moved instantaneously. It is actually an integral over all possible positions and times for the two events, e-/photon and e+/photon so in some cases it is a virtual electron moving one way and a virtual positron moving the other way. In all cases electron charge is conserved on all time slices since there is always one e- and one e+ present (with or without photons) or only photons. The energy and momentum are explicitly and exactly conserved at all points.
Hoping this helps! Peter E. Hughes, Ph.D., Milford, NH
There are two ways to represent antimatter. One is to reverse almost everything and treat it as moving forward in time. Another is to reverse nothing and treat it as moving backward in time. There is no difference in how such a particle would behave, how such a particle would be measured. The second representation is much easier to work with, much easier to calculate. As no measurement can show that one or the other must be true, science prefers to use the simpler model whenever possible.
Dr. Ken Mellendorf
Illinois Central College
Thanks for the question. Time moves forward in Feynman diagrams. The arrows point for anti-particles point in the opposite direction due to the "complex conjugate" operation in the mathematical model. If I take the complex conjugate of the complex number 3+6i, it becomes 3 - 6i. This operation introduces the negative sign and can be thought about as causing the time arrows to point in the opposite direction for anti-particles.
Anti-particles and particles have the same magnitude of the spin (angular momentum). Remember, that Feynman diagrams are simply a pictorial way of representing perturbation theory. That is the reason why Feynman used them.
I hope this helps. Please let me know if you have more questions.
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