HW7 - rules. (2) Prove the following identities involving...

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PHY5667 Problem Set #7 (due Tue Oct 12) (1) Consider a relativistic QFT for a neutral scalar Φ and a charged scalar φ , with the Lagrangian L = 1 2 ( μ Φ)( μ Φ) + ( μ φ )( μ φ ) - M 2 2 Φ 2 - m 2 φ φ - κ Φ φ φ - λ 4 φ φ φφ. In perturbation theory, draw relevant Feynman diagrams and compute amplitudes for the following processes: (i) The decay process Φ φ + φ (one diagram). (ii) The scattering process φ + φ φ + φ (three diagrams). (iii) The scattering process φ + φ φ + φ (three diagrams). If you don’t feel comfortable with Feynman diagrams yet, you can also compute the ampli- tudes algebraically using the operation. In that case, be sure to perform all integrals appearing in your expressions, and be sure to interpret the final results in terms of Feynman
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Unformatted text preview: rules. (2) Prove the following identities involving and , where = = 1 and 1 , 2 , 3 =- 1 , 2 , 3 : (i) + = 2 1 , where the Minkowski metric is given by ( ) = diag(1 ,-1 ,-1 ,-1). (ii) 2 = * 2 . (iii) For an arbitrary 4-vector a , ( a )( a ) = a a 1 . (3) Show that the Lagrangian L = i R R-m 2 T R 2 R-m * 2 R 2 * R gives the equation of motion i R-m * 2 * R = 0 . 1...
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This note was uploaded on 12/14/2011 for the course PHY 5667 taught by Professor Okui during the Fall '10 term at FSU.

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