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The classical scalar field

This chapter explains some of the properties of scalar fields, which are paradigmatic in relativistic field theory. It also shows how a complex scalar field can confer an effective mass to a ‘gauge’ field. The chapter first provides the Klein–Gordon equation derived from the Euler–Lagrange equations outlined in the previous chapter. It then illustrates the Fourier transform of a free field, before embarking on further discussions on complex fields, charge, and symmetry breaking. Finally, this chapter considers that the fact that global symmetry breaking leads to the appearance of a massless, and therefore long-range, scalar field is problematic because such a field is not observed experimentally. It thus takes a look at the BEH mechanism (named after its inventors, Robert Brout, François Englert, and Peter Higgs), which can make it ‘disappear’.