Consider the Lagrangian density of a charged spin 0 scalar field mc. L = * a"- () 6*6. Consider a charged s = 0 field particle interacting with the electromagnetic field. Explain why the following Lagrangian density describes the system: mc. C = [(( + i)o)*(0 + iA)6 - (C)66] - FF. Consider now a local phase transformation: o(x) o' (x) = eiga(2") (24). Show that if at the same time + A = Aw + h, the Lagangian density above is invariant. What is this local symmetry called?