Beyond particle physics, Sternberg applied group theory to statistical mechanics. With Kostant, he showed that the thermodynamic limit of a large system can be understood via — specifically, the group SU(N). This revealed deep connections between phase transitions and symmetry breaking, where the moment map becomes the expectation value of the order parameter.

Before Sternberg’s pedagogical contributions, group theory was often treated by physicists as a bureaucratic necessity—a classification scheme for particles, useful for labeling quantum numbers like spin or isospin, but ultimately distinct from the "real" work of solving differential equations. Sternberg shattered this illusion. He demonstrated that the group is the physics.

in 1994, with a widely available paperback edition released in September 1995. Cambridge University Press & Assessment

But the real physics payoff came when Sternberg applied group theory to gauge theories. Consider electromagnetism: the gauge group ( U(1) ) acts locally. But the global structure of the group—its topology—determines magnetic monopoles. Sternberg showed that the same cohomological ideas that explain fermion phases also classify the obstructions to defining a global gauge potential.