Electromagnetic Interaction The electron and the photon are the key players. The photon transmits the electromagnetic interaction from one electron to the other. That will be the blueprint for all other interactions. electron photon Ch

The photon and electron fields The photon field originates from Maxwell’s equations. The electron field originates from the Dirac equation, the relativistic generalization of Schrödinger’s equation. The Dirac equation contains two new features: - Antiparticles (the positron) - Spin (an internal rotation) The spin of the electron can have two values (±½). They correspond to clockwise or counter-clockwise rotation. As a result, the Dirac equation has four components: {electron +½, electron -½, positron +½, positron -½ }

m 0  0 m 0 = 0 Charged Neutral Spin ±½ Spin ±1 Two opposites Electron Photon Fermion Boson

Fermions:Particles with half-integer spin. Bosons:Particles with integer spin. The electron is a fermion, the photon a boson. The quarks are fermions, the gluons are bosons. General diagram for all the interactions: Bosons transmit an interaction from one fermion to another. Fermions versus Bosons fermion boson

Fermions are loners. They obey Pauli’s exclusion principle which forbids two fermions to be at the same place at the same time. Therefore two fermions cannot have the same quantum numbers. Bosons are social particles. They like to be together, for example photons in a laser. They communicate between lonely fermions. Pauli’s exclusion principle Enrico Fermi Wolfgang Pauli Satyendra Bose

The electromagnetic coupling constant  The coupling constant  gives the strength of an interaction. It is proportional to the square of the unit charge e, because e appears twice in the basic diagram for the interaction. In units of ħ and c one obtains a simple but mysterious number: e e ‘All good theoretical physicists put this number up on their wall and worry about it.’ Richard Feynman  = e 2  1 137

Feynman diagrams provide an elegant way to simplify the complicated calculations by starting with a few particles. To increase the accuracy one needs to add extra particles. The diagram on the right contains an additional photon. It causes a slight increase in the electron’s magnetic field. Manybody calculations

Quantum electrodynamics has produced some of the most accurate experimental tests in physics. An example is the magnetic field of the electron. Precise calculations Some of the many Feynman diagrams used for a precise calculation of the electron’s magnetic field. Computers handle thousands of such diagrams to provide high precision.

Magnetic field strength of the electron in units of e/2m e c ±3 in the last digit Extra part due to diagrams with additional “virtual” particles. Agrees with the calculation. Coupling constant  1 / ±4 in the last digit Precise measurements Fundamental Physical Constants from NIST

It is possible to keep a single particle in a trap where is can live undisturbed for a year. This trap uses combined electric + magnetic fields. Trapping a single particle Priscilla, the lonely positron