lecture16-17

lecture16-17 - Lecture 16-17 Notes: 07 / 27 and 07 / 28...

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Lecture 16-17 Notes: 07 / 27 and 07 / 28 Particle physics Quantum electrodynamics On a microscopic level, electromagnetic interactions between electrons can be viewed as the electrons exchanging photons. One electron emits a photon, and another absorbs it: A drawing like this is called a Feynman diagram . It corresponds to a well-defined mathematical expression that can be used to determine the probability of the electrons interacting in a particular way. Note that this is somewhat similar to a diagram for a chemical reaction that has two electrons in the initial and final state, and two electrons and a photon in the intermediate state: The photon allows for transfer of energy and momentum between the two electrons. We label the electrons' initial 4-momenta P 1 and P 2 , the final 4-momenta Q 1 and Q 2 , and the 4-momentum of the photon K : The 4-momentum is conserved at every vertex (point of interaction between a photon and an electron): if an electron emits a photon with 4-momentum K , its own 4- momentum decreases by K , while the 4-momentum of the electron that absorbs the photon is increased by K . This ensures that the 4-momentum for the overall process is conserved: Q 1 + Q 2 = P 1 + P 2 .
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The photon appears as an intermediate in the process, but not in the initial or the final state. Intermediate particles like this are known as virtual particles . Particles that are actually observed either in the initial or in the final state are known as real particles . Real particles obey the energy-momentum relationship E 2 = p 2 c 2 + m 2 c 4 ( E = pc for the massless photon), but the energy and momentum of virtual particles can deviate from this relationship. However, the process depicted in the diagram is more likely to occur for small deviations than for large ones. Because the energies and momenta of the electrons change due to the exchange of the photon, the paths of the electrons change direction as a result of this reaction. Calculating exactly how the photons and electrons behave from the Feynman diagrams gives the same results as classical electrodynamics, provided we look at the average behavior of a large number of photons and electrons rather than individual particles. Anti-particles The arrows on the electron lines show the direction of negative charge flow. If the arrow points to the right (forward in time), then negative charge flows in the direction of the particle's motion, just as we expect for a moving electron. It turns out we can turn the arrow backwards. Then, the negative charge follows in a direction opposite to the particle's motion, which corresponds to a positively charged particle. The positively charged counterpart of an electron is known as a positron . The positron has exactly the same properties as an electron (mass, interactions, etc)
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lecture16-17 - Lecture 16-17 Notes: 07 / 27 and 07 / 28...

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