#### Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II

#### Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I

#### Axial Vector Current Conservation in Weak Interactions

Like bulls in a china shop, physicists can’t leave a pretty thing like a symmetry alone. Half of this year’s physics Nobel Prize recognizes Yoichiro Nambu of the University of Chicago for showing that broken symmetry can lead to the creation of mass for fundamental particles. His work, published in *Physical Review Letters* and *Physical Review* in 1960 and 1961, was an important precursor to the theory that unifies electromagnetic and weak forces, and similar symmetry breaking is central to most modern particle physics theories.

Symmetries are not hard to find. Plates in the china shop look the same when rotated; serving platters are identical to their mirror reflection. But much of the world is messy and asymmetric, and discovering how certain symmetries are violated, or broken, can reveal deeper physics.

Nambu developed a mathematical mechanism for spontaneous symmetry breaking in particle physics. Spontaneous symmetry breaking occurs in systems that under certain conditions are symmetric, but whose lowest energy state is not. A classic example is a hot chunk of magnetic material, in which the atomic-scale “bar magnets” point in random directions, making its interior symmetric under rotation. But as the material cools, these elements align in a single direction, and the metal becomes magnetized. The rotational symmetry is broken in this lowest energy configuration, hiding the symmetry that still exists in the equations of electromagnetism.

Something similar happens in a superconductor. At high temperature, the electrons in the material are free to roam around randomly, but below a critical temperature their lowest energy state is one in which they pair up. Nambu modeled this behavior in the context of quantum field theory. He was able to explain the expulsion of magnetic fields by superconductors in a new and elegant way involving the breaking of symmetry in the field equations when electrons pair up [1].

This analysis set the stage for Nambu’s Nobel Prize winning work, in which he applied the superconductivity formalism to the physics of protons, neutrons and other strongly interacting particles. In this case, Nambu was dealing with so-called chiral symmetry, which involves the spin and momentum of massless particles and is broken for particles with mass.

Nambu imagined massless particles with a simple, chirally-symmetric equation describing their motion and interactions. He then assumed that the lowest energy state of the system–the formula for the possible configurations of particles and fields–was asymmetric, like the low-temperature piece of magnetic material. So the inherent symmetry in the fundamental equations was hidden. In this state, it turned out that the particles had mass, and a new, light particle appeared that looked a lot like the pion, the lightest of the strongly-interacting particles. “Because pions arise from the model in this peculiar way, you can derive several properties about them,” explains Roman Jackiw, a particle physicist from MIT who has written about Nambu’s work before. For instance, Nambu and his collaborators could compute the interaction strength between pions and nucleons (protons and neutrons).

Once the quark model was developed, pions played a less fundamental role, and most other details of Nambu’s model were later superseded. But he showed how to connect the highly symmetric, massless particles that appear in the underlying particle theories with the massive particles observed in the real world. The idea was later incorporated into the so-called Higgs mechanism, which was part of the unification of electromagnetic and weak forces into a single theory and a central tenet of the standard model of particle physics. Particle masses are thought to come from interactions with the Higgs particle, which arises out of the breaking of another symmetry. “His work was deep and original and he was well-ahead of his time,” says Helen Quinn from the Stanford Linear Accelerator Center.

“All theories of particle physics–even new ones like supersymmetry and string theory–use spontaneous symmetry breaking,” Jackiw says. Besides greatly simplifying calculations, “it is satisfying for most physicists to think that nature at its ultimate roots is symmetric,” he says.

Michael Schirber is a freelance science writer in Lyon, France.

### References

- Y. Nambu, ”Quasi-Particles and Gauge Invariance in the Theory of Superconductivity,” Phys. Rev. 117 648 (1960).