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Electron capture feynman diagram12/29/2023 ![]() ![]() Feynman (Princeton University Press, 1985) There is no complicated formula for the amplitude of an electron to emit or absorb a photon it doesn’t depend on anything – it’s just a number!Īdapted from QED – The Strange Theory of Light and Matter by Richard P. Every coupling, therefore, is a junction between two straight lines and a squiggly line. We will call this action a “junction” or “coupling.” (This is the point where the squiggly and straight lines meet in the diagram above.) To distinguish electrons from photons in the diagrams, electrons will be depicted going through space-time as a straight line. The third basic action is: an electron emits or absorbs a photon – it doesn’t make any difference which. However, you might be interested to know that the formula for P(A to B) – a photon going from place to place in space-time – is the same as that for E(A to B) – an electron going from place to place – if n is set to zero. It is a rather complicated formula, and the really isn’t a way to explain it in simple terms. In reality, electrons have a type of polarization, which doesn’t add anything to the main ideas it only complicates the formulas a little bit.) The formula for the amplitude for this action, which we will call E(A to B) also depends on (X2 – X1) and (T2 – T1) as well as on a number we will call n, a number that, once determined, enables all our calculations to agree with experiment. (For the moment we will imagine this electron as a simplified, fake electron, with no polarization – what the physicists call a “spin-zero” electron. The second action fundamental to quantum electrodynamics is: a n electron goes from point A to point B in space-time. However, when the distances are short these other possibilities become vitally important and must be considered. The amplitudes for these possibilities are very small compared to the contribution from speed c in fact, they cancel out when light travels over long distances. It may surprise you that there is an amplitude for a photon to go at speeds faster or slower than the conventional speed, which is called c. Light doesn’t go only in straight lines nor does it always go only at the speed of light! The major contribution to the size of the arrow (which we call P(A to B)) occurs at the conventional speed of light – when (X2 – X1) is equal to (T2 – T1) – where one would expect it all to occur, but there is also an amplitude for light to go faster (or slower) than the conventional speed of light. (You may recognize this as part of the Pythagorean Theorem – which in this case would actually involve three terms representing the x, y, and z-axis.) These differences can be expressed mathematically as (X2 – X1) and (T2 – T1). It depends on the difference in distance and the difference in time between the beginning and ending points of the line. It is one of the great laws of Nature, and it’s very simple. There is a formula for the size of this line. (This is illustrated above a wiggly line for no good reason – it is just an arbitrary depiction.) More accurately, it should be said that a photon is known to be at a given place at a given time and has a certain amplitude to get to another place at another time. Now, let’s look at the first basic action in detail – a photon goes from place to place. All of the particles (both the electrons ( ) and the photon ( )) represented in the diagram move through time and space. The x-axis (left and right) represents space. Since we will be dealing with photons and electrons, which move very rapidly, a 45 degree angle represents something going the speed of light (the squiggly line). Along the y-axis (up and down) is the time scale. Illustrated above is an animated Feynman Diagram depicting the three basic actions which can occur. Its path changes and it travels to point 4 where it leaves the graph.Īnd for those who want a bit more detail… ![]() Another electron starts out at point 2 where it travels through space-time to point 6 and absorbs the photon emitted by the first electron. So in simple terms, what does this diagram depict? It shows an electron, which starts out at 1 and moves through time-space to point 5, where it emits a photon, altering its path and moving along to point 3 where it goes off of the graph. The third, an electron emits or absorbs a photon, is illustrated by the junctions at points 5 and 6. The second, a n electron goes from point A to point B in space-time, is illustrated by the lines from 1 to 5, 5 to 3, 2 to 6, and 6 to 4. The first, a photon goes from place to place, is illustrated by the line from 5 to 6. ![]()
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