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.
, are introduced simultaneously with mathematical concepts like homomorphisms representation theory Advanced Topics : It covers compact groups Lie groups , and the significance of the elementary particle physics Historical Context sternberg group theory and physics new