The Physics of Quantum Electrodynamics
Introduction
Quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.
History and Development
The development of QED was a major feat of 20th-century physics, initiated by the work of Dirac, Heisenberg, and Pauli in the late 1920s. The theory, as we know it today, was formulated by Feynman, Schwinger, and Tomonaga during the 1940s and 1950s. For their contributions to the development of QED, Feynman, Schwinger, and Tomonaga were jointly awarded the Nobel Prize in 1965.
Basic Principles
QED is a theory that combines quantum mechanics and special relativity to explain the interactions between photons and charged particles, such as electrons and positrons. It is based on the assumption that interactions between particles are mediated by force-carrying particles. In the case of QED, these are photons, the particles of light.
The basic principles of QED can be summarized as follows:
- Charged particles (e.g., electrons and positrons) can emit or absorb photons, which carry the electromagnetic force.
- The probability of an event occurring can be calculated by summing up the contributions of all possible paths of the particles involved.
- The behavior of particles in QED is described by wave functions, which are solutions to the Schrödinger equation.
- The interactions between particles are described by the exchange of virtual photons, which do not need to obey the energy-momentum relation of real photons.
Mathematical Formulation
The mathematical formulation of QED is built upon the principles of quantum mechanics and special relativity. It involves the use of complex numbers and matrices, and requires a good understanding of differential equations and Fourier analysis.
The key equations of QED are the Dirac equation, which describes the behavior of fermions (particles with half-integer spin), and the Maxwell's equations, which describe the behavior of electromagnetic fields. These equations are combined into the QED Lagrangian, which is used to calculate the probabilities of different outcomes in particle interactions.
Applications and Experiments
QED has been tested in numerous experiments and has been found to be extremely accurate. Its predictions have been confirmed to a precision of a few parts in a billion in some cases. Some of the most notable experiments validating QED include the Lamb shift experiments, the g-2 experiments, and the measurement of the anomalous magnetic moment of the electron.
In addition to its fundamental importance in physics, QED also has practical applications. For example, it is used in the design of lasers and LEDs, in the analysis of electron scattering experiments, and in the calculation of atomic energy levels.