solutions 07

# Introductory Nuclear Physics

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• davidvictor
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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 ½ m ² A μ A μ does break the usual gauge invariance of the electromagnetic field in that a "shift" transformation of the field A μ A μ ' = A μ + μ χ / q does not leave the term invariant. Hints: no hints Solution: no solution yet Problem VII.2 Consider the gauge transformation φ φ ' = e i α φ and A μ A μ ' = A μ + μ α / q . If φ satisfies the equation ( D μ D μ + m ²) φ = 0, with D μ = μ - iqA μ , derive the equation that is satisfied by φ ' . Hints: no hints Solution: no solution yet Problem VII.3 Consider the complex scalar field Schrödinger Lagrangian L = i ( φ / t ) φ * - φ · φ */(2 m ). Treating the fields φ and φ * as independent, derive the equations of motion for these fields and show that they are indeed the usual Schrödinger equations, and that they are consistent, i.e. they are each other's complex conjugates. Hints: no hints Solution: no solution yet phy431_s99_hw07 (1 of 2) [4/10/2000 4:36:04 PM]

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• Spring '01
• Rijssenbeek

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