Symmetry Breaking on a Supercomputer

This article is a month old, but better late than never.

One of the points that I've always tried to get across is that fields such as condensed matter physics, which many physicists who study "fundamental" issues look down upon, can and have made significant contribution to the fundamental issues in physics. This article on spontaneous symmetry breaking in lattice QCD is one such example.

Chiral symmetry distinguishes right-hand spinning quarks from left-handed and is exact only if the quarks move at c and are therefore massless. In 1961 Yoichiro Nambu and Giovanni Jona-Lasinio proposed the idea of SCSB, inspired by the Bardeen–Cooper–Schrieffer mechanism of superconductivity in which spin-up and spin-down electrons pair up and condense into a lower energy level. In QCD a quark and an antiquark pair up, leading to a vacuum full of condensed quark–antiquark pairs. The result is that chiral symmetry is broken, so that the quarks – and the particles they form – acquire masses.

This is not the first such case, and in fact, not the only time the Nambu et al. work has inspired a development in something fundamental. Peter Higgs made the same leap using Nambu's work and later on, took up Phil Anderson's work on Goldstone boson to come up with what we now called the Higgs mechanism.

"When I moved back to Edinburgh in October 1960 I was not sure where I was going next," he recalls. That all changed the following year when he read a paper by Yoichiro Nambu that based a theory of elementary particles on an analogy with the BCS theory of superconductivity. "This is where the idea of a spontaneously broken symmetry being the way in which the mass of particles could be generated first arose," says Higgs. "Although my name gets thrown around in this context, it was Nambu who showed how fermion masses would be generated in a way that was analogous to the formation of the energy gap in a superconductor."

There was, however, a problem with the Nambu approach. Although the spontaneous breaking of symmetry generated particles with mass, Jeffrey Goldstone, Salam and Steven Weinberg had shown that it also generated a particle known as a Goldstone boson that had no mass. This was bad news because no such particle was known to exist.

Once more help arrived from the condensed-matter community when, in 1963, Phil Anderson pointed out that the equivalent of a Goldstone boson in a superconductor could become massive due to its electromagnetic interactions. But did Anderson's argument apply in the relativistic case? No, said a paper by Walter Gilbert in an issue of Physical Review Letters that arrived in Edinburgh the middle of July. Yes, said Higgs, after thinking about it over the weekend.

There you go. These are clear proofs that many of the fundamental ideas and principles of world can come from a field of study that deals with materials and many-body interactions. So kids, you don't have to be string theorists, astrophysicists, or study high-energy physics to make significant contributions to our basic understanding of the universe.

Zz.