Spontaneous Symmetry Breaking
Now suppose that the potential has a minimum not at but at some non-zero value . This can happen if one writes (for example) and then sets to an imaginary value. In this case, one says that the Lagrangian exhibits spontaneous symmetry breaking. The non-zero value of is called the vacuum expectation value of . In the Standard Model, this non-zero value is responsible for the fermion masses, as shown below.
To exhibit the mass term, one re-expresses the action in terms of the field, where is now understood to be a constant independent of position. We now see that the Yukawa term has a component
and since both g and are constants, this term looks exactly like a mass term for a fermion with mass . This is the mechanism by which spontaneous symmetry breaking gives mass to fermions. The field is known as the Higgs field.
Read more about this topic: Yukawa Interaction
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