Breaking a Quantum Symmetry on the Tabletop

A recurrent theme in art and science, the concept of symmetry has become a powerful scientific tool for the analysis of physical systems. However, under special circumstances, a "quantum anomaly" occurs: the laws of quantum physics break a system's apparent symmetry.

After a long search, a research group (Horacio Camblong, University of San Francisco, camblong@usfca.edu, and collaborators at Universidad Nacional de La Plata, Argentina) has found a relatively simple example of a quantum anomaly: the interaction of a polar molecule with an electron. A polar molecule, despite being neutral, has a permanent separation of electric charge--a dipole. This dipole produces an electric field, which can capture electrons if it is strong enough.

Can such an arrangement exist as a stable ion, with its "extra" electron? The researchers formulated the answer to this question in the language of symmetry. In physics, symmetry means that a system, such as the molecule-electron arrangement, behaves the same after you perform a change to it, such as stretching the molecule to larger scales and making appropriate adjustments to other variables in the system.

At first glance, the electron-molecule interaction exhibits a remarkable scale invariance: the system "looks" the same when viewed from different scales in space and time--at least in a classical physics description which treats the molecule as a dipole and the electron as a point of charge.

But this tidy picture breaks down with a proper treatment of the system, as prescribed by quantum field theory. A quantum field theory treatment requires the process of renormalization, which removes certain mathematical infinities and inconsistencies from the quantum approach. This process also makes the molecule's energy levels discrete or quantized rather than continuous.

Examining the system this way, the researchers found that the scale invariance broke down. In fact, a large body of existing evidence, both experimental and numerical, supports their conclusion. While all other known quantum anomalies occur at high energies (an example is chiral symmetry in nuclear physics), the work suggests that quantum symmetry breaking can occur at much lower energies, in the domain of interacting electrons and molecules. (Camblong et al., Physical Review Letters, 26 November 2001; for a discussion of symmetry breaking in physics, with examples, see paper by Barry Holstein of University of Massachusetts at Amherst.)