Introductory Nuclear Physics

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PHY431 Homework Set 8 Reading: Lecture Notes Homework: See below: Due date: Wednesday April 26 Hints and Solutions Problem VIII.1 Find the expression for the "Dirac Potential" V D in the Dirac equation i ψ / t = (- i α · + β m + V D ) by using the principle of minimal substitution to the free fermion Dirac equation. Hints: Note that V D must be a 4×4 matrix operator. Solution: no solution yet Problem VIII.2 Verify that the spinor contraction (dot product with itself) u + u equals 2 E ( E + m ) for u (1) and for u (2) . Note that u + stands for transpose and complex conjugation.
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Unformatted text preview: Hints: no hints Solution: no solution yet Problem VIII.3 Find the matrix expression for γ 5 in the Dirac representation. Hints: See equation 12.19 in the notes. Solution: no solution yet Problem VIII.4 Given the definition 5 ≡ i 1 2 3 and the anticommutation relations for the gamma matrices, prove that P L μ = P R . 1. Show that f8e5ψ L = P R 2. phy431_s00_hw08 file:///C|/DOCUME~1/PHY_CO~1/PHY431/PHY431_S00_hw08.HTML [4/18/2000 10:48:41 PM]...
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