Why String Theory? by Joseph Conlon

Author:Joseph Conlon
Language: eng
Format: epub
Publisher: CRC Press
Published: 2018-01-31T00:00:00+00:00

8.4 APPLICATIONS TO CONDENSED MATTER PHYSICS

The quark-gluon plasma belongs to particle physics, and quantum field theory is certainly a major part of particle physics. Quantum field theory has however spread its affections widely, and it is a subject with many lovers.

In particular, it is also pervasive throughout condensed matter physics. This is the branch of physics that describes phases of matter, both common and uncommon, that consist of lots and lots and lots of atoms. These include old favourites from school such as solids, liquids and gases, but also more exotic examples such as superconductors and topological insulators. These different phases have radically different properties and can behave in bizarre ways. What they have in common is that their meaningful existence requires many atoms to be present.

Confronted with a lone atom, it makes as much sense to regard it as a liquid atom or a solid atom as it does to view it as a rat atom or an elephant atom. By itself, it is just an atom. When many atoms are put together though, the behaviour of the collective exhibits distinctive properties. This is directly analogous to the movements of a crowd at a music festival or the flight of a murmuration of starlings. For this reason, condensed matter physics is also often called many-body physics. It is the science of how macroscopic properties of matter arise from the collective microphysics of large numbers of atoms.13

The number of bodies – atoms or molecules – involved in typical macroscopic systems is not just large. It is enormous. A glass of water contains enough atoms to put ten thousand of them on every square millimetre of the earth’s surface. If we tried to write down the equations for each atom, the sun would be dead and cold before we were one millionth of the way through. The differences between solids and liquids, real as they are, cannot be found by direct assault on the equations of each individual atom.

This is an old problem, with a history that predates the advent of quantum mechanics. The motion of an ideal gas – separate individual atoms interacting with the rigid formality of billiard balls – was understood in Victorian times. This was a classical problem, but in many cases it is now necessary to consider the simultaneous effects of both quantum mechanics and the presence of many bodies. For close-packed atoms in a solid, with an average separation of somewhere around a nanometre, the distances are small enough that quantum mechanics cannot be ignored.

The study of quantum many-body systems has been carried out by many fabulously smart people over many decades. I will not and could not review it in any detail. Much of it is too tangential to this book, and my knowledge of the history is only of the mythological kind produced by textbooks and the names of Nobel Prize winners. I move straight to two important and relevant conclusions: first, quantum mechanics is essential, and second, quantum field theory is essential.

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