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Unformatted text preview: PHY431 Homework Set 7 Reading: Lecture Notes Homework: See below: Due date: Wednesday April 19 Hints and Solutions Problem VII.1 Show that a mass term of the form m A A does break the usual gauge invariance of the electromagnetic field in that a "shift" transformation of the field A A ' = A + / q does not leave the term invariant. Hints: no hints Solution: no solution yet Problem VII.2 Consider the gauge transformation ' = e i and A A ' = A + / q . If satisfies the equation ( D D + m ) = 0, with D = - iqA , derive the equation that is satisfied by ' . Hints: no hints Solution: no solution yet Problem VII.3 Consider the complex scalar field Schrdinger Lagrangian L = i ( / t ) * - */(2 m ). Treating the fields and * as independent, derive the equations of motion for these fields and show that they are indeed the usual Schrdinger equations, and that they are consistent,...
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