This article is sort of a continuation of the article on quarks. That one focused on quarks and the theory of its interactions, Quantum Chromodynamics. This article will focus on electrons and the theory of electromagnetism on a small scale and the theory of Quantum Electrodynamics (QED). Feynman, one of the founders of this theory, called it the ‘Jewel of Physics’ for its incredibly accurate predictions. Such accuracy has never been seen before. It predicted some observations accurately to thirteen decimal places!
The electron is a fundamental particle with a unit negative charge and an incredibly small mass. It is a lepton with a spin of magnitude half. The idea of spin is pretty hard to grasp, it is not like the usual classical idea of a spinning object, that cannot happen as calculations show that an electron has to spin at a speed faster than the speed of light. Spin, essentially means that a particle has a non-zero value of angular momentum just by the virtue of existence. Electrons are fermions, which implies that electrons are subject to the Pauli Exclusion Principle; no two electrons in the universe can have the same magnitude of energy. Like gluons in QCD, the carriers of electromagnetic force are virtual photons. Virtual particles are those that do not exist, that is, while we can’t physically show the existence of the particle, we can feel its effects.
First, a note on fermions and bosons. As I mentioned, the Pauli Exclusion Principle applies only to fermions, or particles with half-integral spin, and not to bosons, with integral spin. This idea is purely mathematical, so there’s really not much to explain. The effective wavefunction of fermions is anti-symmetric while, for bosons, it is symmetric. This basically means that if you have a wavefunction of two bosons, and you interchange the bosons, then the wavefunction still remains the same. However, in case of a wavefunction for two fermions, if you switch them, then the wavefunction picks up a negative sign.
Electrons (and other fermions) exhibit an interesting phenomenon, the formation of Cooper pairs. At very low temperatures, two electrons come together and behave as one bound pair. The energy of formation of a cooper pair is very low, so thermal excitations can easily break up the pairs. The electrons in the pair don’t have to be in contact, they behave as one pair even over long distances, like up to hundreds of nanometers. An electron in a metal normally behaves as a free particle. The electrons mutually repel each other and attract the positive ions that make up a metallic lattice. This attraction distorts an ionic lattice, moving some of the ions slightly toward the electron. This increases the positive charge density of the lattice in the vicinity of the electron. This positive charge can attract other electrons. Over long distances, the attraction between electrons due to the displaced ions can overcome the inter-electronic repulsion and can thus pair up. This is at best a semi-classical explanation of the effect. The actual quantum mechanical explanation is much more rigorous and requires a lot of mathematics so I won’t be going into that.
An interesting phenomenon in this theory is the idea of vacuum polarization. The measured charge of an electron is lesser than its actual charge. Because of the charge of the electron, it has its own electric field. Now, the existence of an electric field means that there is more energy in that region than there would be without the electron. This leads to the spontaneous formation of particle-antiparticle pairs around the electron for a short duration of time. However, since this process happens near the electron as long as it is present, it leads to the electron being perpetually surrounded by a covering of particles. The existence of this layer of particles damps out the charge on the electron, and thus the charge that we observe is lesser than the actual charge on the electron.
Before I discuss the positron, I want to mention one last very interesting phenomenon that is only shown by electrons. This is called spin-charge separation. Basically, under certain conditions, the spin and charge on an electron split up. That is, one electron exhibits only charge, and the other electron exhibits only the spin. No electron can exhibit both these properties. An electron, by itself, has charge and spin. Another way looking at this is that the electron itself is bound to the state of two particles, the spinon (carries the spin) and the chargon or holon (carries the charge). An electron in a bound system also has a third particle, the orbiton (carries the orbital angular momentum). In our case, we consider an electron as a bound state of a spinon and chargon. Under certain conditions these particles can become deconfined, that is, they break free and behave as individual particles. These particles, the chargon, orbiton and the spinon are called quasi-particles.
The antiparticle of an electron is the positron, with a unit positive charge. All other properties remain the same. The existence of antiparticles leads to an interesting effect termed as ‘Zitterbewegung’, which is German for ‘trembling motion’. When the relativistic effects are taken into consideration and the wavefunction of an electron is formulated, then, it is observed that the wave-packet solution of the electron interacts with the positron wave-packets, which occupy the negative energy states and this gives rise to rapid oscillations. These oscillations occur with the speed of light. On a side note, this effect is observed not only with electrons but with the relativistic hydrogen atom and has been observed in Bose-Einstein-Condensates (BECs).
QED is one of the only theories that we understand to a great extent, yet there is a lot to be done, in the larger scheme of things. This is just the starting point in the quest to find a Grand Unified Theory.