Scattering - quantum electrodynamics

[lntz]

hi,

so i have just finished reading my first ever book on quantum electro-dynamics (the feynmann lectures). i am in year 13 of school, or High school some might call it.

he draws a diagram in the book (a space time diagram) to represent an electron absorbing a photon and then re-emitting the photon, this is what i understand as scattering. however he also draws diagrams that show the electron emitting a photon before it has even absorbed the photon in question!

my understanding is that an electron is a fundamental particle, so it shouldn't really contain a photon to emit, unless it had already absorbed one... (i know that the photon is essentially just energy inside the electron).

so does the electron actually have to travel backwards through time after absorbing the photon (as the diagram suggests) to re emit it or is there some other mechanism that goes on here?

i'm just confused as to whether this electron has physically traveled backwards in time, or whether it is just how the mathematics is arranged...

please let me know what you think :)

lntz.

 

[A. Neumaier]

hi,

so i have just finished reading my first ever book on quantum electro-dynamics (the feynmann lectures). i am in year 13 of school, or High school some might call it.

he draws a diagram in the book (a space time diagram) to represent an electron absorbing a photon and then re-emitting the photon, this is what I understand as scattering. however he also draws diagrams that show the electron emitting a photon before it has even absorbed the photon in question!

my understanding is that an electron is a fundamental particle, so it shouldn't really contain a photon to emit, unless it had already absorbed one... (I know that the photon is essentially just energy inside the electron).

so does the electron actually have to travel backwards through time after absorbing the photon (as the diagram suggests) to re emit it or is there some other mechanism that goes on here?

No. Photons are not in electrons and electrons cannot absorb photons.
Feynman diagrams are not depicting what is absorbed or emitted.
And nothing travels backward in time - this was useful imagery around 1948 when Feynman invented his calculus, but has only very limited value and doesn't really contribute to understanding what actually happens.

Elementary particles (photons and electrons) are elementary excitations of the corresponding quantum fields, and are best understood as harmonic modes. Just as a resonating string can sound not at all (no particle), in the basic mode (1 particle = 1 extremum per length), in the first overtone (2 particles = 2 extrema per length), in higher overtones (k particles = k extrema per length) or in a superposition of these (a Fock state - superposition of different particle number states). Indeed, Fock space, which is the mathematical framework in which one commonly defines QED, is defined by the harmonic analysis of a free wave equation, the
4-dimensional analogue of the differential equation describing an idealized string of a guitar.

Two kinds of particles correspond (in this analogy) to two strings (with an associated tensor product state space). E.g., two electrons and a photon = first overtone on first string and basic mode on second string.

Now a guitar is has interactions between its modes (mainly through its resonating body),
hence produces complex sounds. Similarly, QED (which has in place of six strings fields with three kinds of particle excitations - electrons positrons and photons) produces a complex behavior of the states of the quantum fields, to which many particle modes may contribute.

Feynman diagrams tell you how a complex state (i.e., sound in the analogy) can be decomposed into elementary interactions - namely the vertices of the diagrams. There are only very few kinds of them, in QED essentially only one, which depending on how it is viewed, takes several possible interpretations:
- an elementary interaction can change a virtual electron into a virtual electron and a virtual photon or a virtual electron plus virtual photon into just a virtual electron (i.e., the wave on the first string can affect the overtone number of the second string),
- a virtual positron can do the same,
- a virtual electron and a virtual positron can annihilate, changing into a virtual photon, or
- a virtual photon may change into a virtual electron-positron pair.

All this is virtual, just internal book-keeping of the decomposition process by which the physicist creates a picture of what happens in Nature (without all this imagery, which is special to Feynman's approach to QFT). Note that most single diagrams are meaningless (giving rise to so-called infinities or divergences); many such diagrams simultaneously are needed (and must be ''summed'') to describe a real process - though in some import cases a few of them give a reasonable approximation.

Real (which means observable) are only the free ends of the Feynman diagrams - these correspond to real particles (satisfying physical laws such as energy and momentum conservation). As the ends have a direction, this tells you what may come in and what may go out, namely the input and output of real scattering events. And then there is an elaborate machinery that turns the collection of _all_ Feynman diagrams with the same collection of ends into a recipe for calculating highly accurate probabilities for these events.

Thus scattering is _not_ what happens inside a single Feynman diagram, but what happens when you take all Feynman diagrams with the same input and output together.