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, firstname.lastname@example.org, 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
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.)