Quantum electrodynamics (QED), is a fundamental scientific theory that is also known as the quantum theory of light. Because Feynman diagrams allow physicists to depict subatomic processes and develop theories regarding particle interactions, the diagrams have become an indispensable and widely used tool in particle physics.įeynman diagrams derive from QED theory. Moreover, Feynman diagrams allow visual representation and calculation of the ways in which particles can interact through the exchange of virtual photons and thereby provide a tangible picture of processes outside the human capacity for observation. With regard to QED theory, Feynman is perhaps best remembered for his invention of what are now known as Feynman diagrams, to portray the complex interactions of atomic particles. If higher order diagrams (integrals) are sufficiently smaller than lower order diagrams, then the series is perturbative.American physicist Richard Feynman ’s (1918 –1988), work and writings were fundamental to the development of quantum electrodynamic theory (QED theory). They also represent the lowest order diagram in a series of diagrams with successively more particles exchanged.Īs each diagram represents the integral for a matrix element, the series of diagrams corresponds to a series of integrals that must be summed to get the entire matrix element. They represent the most basic interaction that transforms the initial state into the final state, and therefore normally involve the exchange of only one photon or one fermion. The Feynman diagrams we have looked at thus far are known as "tree" diagrams. We say that virtual particles are "off the mass shell" while real particles are "on the mass shell". Since virtual particles exist for only a finite time, their energy is uncertain, and the mass is part of the energy of the particle. Giving up the defined mass is justified by Heisenberg's uncertainty relation, DE Dt > hbar/2. This process cannot occur in vacuum for a real massless photon, and conserve energy and momentum simultaneously, as you will demonstrate in a homework problem. This can be readily seen by considering the diagram for a single photon producing an e +e - pair. Virtual particles can have a mass that is different from the mass of their real counterparts. What we give up is the "mass constraint" on virtual particles. However, in doing so we must give up something. It is standard convention to impose energy and momentum conservation at each vertex. Notice that in these processes, the exchanged particle is an electron (fermion) not a photon (boson).Īny particle in a Feynman diagram that is not part of the initial or final state is called a virtual particle. Pair Annihilation, Pair Production, and Compton ScatteringĪ valid Feynman diagram can be reflected and twisted to produce other valid Feynman diagrams.Īn example of this process is given by the three basic diagrams for the processes of pair annihilation, pair production, and Compton scattering. Let's look at some examples, beginning with Bhabha scattering.īhabha scattering is named for the Indian physicist who first calculated the process. Many complex processes can be built from this basic QED vertex. We draw an arrow on the lines to indicate the time sense of the fermion.Īn arrow pointing forward in time identifies that line as a particle.Īn arrow pointing backward in time identifies that line as an antiparticle. The two fermion lines are part of a single, unbroken line. In Quantum Electrodynamics (QED) the basic interaction vertex is the junction of two fermion lines with a photon. This is enough to start with, let's use these to look at a more complex interaction. Lines should be labeled to avoid confusion.Photons are represented by wavy lines, gluons by loopy lines, and Z° or W ± by either wavy lines or dashed lines. Bosons are drawn as dashed lines, wavy lines, or loopy (helix or spring-like) lines.Fermions are drawn as continuous, solid lines.Ī fermion line can end only in the initial or final states (left or right side of the diagram). (Again, some authors draw time in the vertical direction, in which case you can rotate the drawing clockwise by 90° to get our convention.) The left side of the diagram represents the initial state, and the right side represents the final state. The vertical direction represents all other spatial directions. The horizontal direction is the horizontal direction, increasing from left to right.Lecture 12 Recall from last lecture: Rules for Drawing Feynman Diagrams (version one)
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