10 - The Yang-Mills bonanza

Summary

We must now go back to 1954, to a time when the big successes of the theory for the electromagnetic forces between the particles were still fresh. Not yet discouraged by the discoveries of numerous particle species that were yet to come, scientists were still searching for simple, elegant and universal principles in physics.

All aspects of the electromagnetic forces between particles can be deduced from the equations that are obeyed by the electric and the magnetic fields. These fields are vector fields. A ‘vector’ is a quantity that is not only characterized by its strength but also by its direction, and several numbers (typically three) are needed its description. ‘Field’ means that these numbers may have different values at different points in space and time. The wind velocity in the atmosphere could be called a vector field. For the wind, you first indicate how much air is moving northwards (if it moves southwards you give this number a minus sign); secondly, you determine the east—west movement; and finally you give a number corresponding to the vertical component.

Taken all together the electromagnetic field has six components. But these cannot be chosen at will. These numbers are hanging together via ‘field equations’, just like the wind velocity components are related to the air pressure distribution in the neighborhood. If you know the air pressure, you can calculate the wind speed in all directions.