Add a new page:
This is an old revision of the document!
Vacuum expectation values are important to describe the Higgs mechanism and symmetry breaking in general.
In classical field theory, we are interested in the solutions of the Yang-Mills equations and these correspond to critical points of the action.
In contrast, in quantum field theory, we use the action to compute "vacuum expectation values" of observables. A vacuum expectation value is the average measured value in the vacuum state. The thing is that many physically interesting quantities can be expressed as vacuum expectation values through various tricks.