8.324 Relativististic Field Theory II, Assignment 5 Solution
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The gray filled circle represents the coupling of the virtual photon to the target, taking the target from an initial state X to some final state Y , which we incorporate into a scattering amplitude factor ˆ ν (q), where M q = p − p� = k� − k. The full matrix element for the process is: M = (−ie)ū(p�)γμu(p) −igμν ˆ ν (q) (1) q2 M Parts a) and b) of the problem analyze the structure of the ū(p�)γμu(p) piece, the results of which are used in c), d), and e) to find an expression for the cross-section.
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8.324 Relativististic Field Theory II, Assignment 1 Solution
(a) Since the generators Ta are Hermitian, the transformation laws are δψ = iǫaTaψ (2) δψ̄ = −i ̄ Ta ψǫa (3) The Lagrangian is quite trivially seen to be invariant δL = −iδ ψ̄(∂/ −m)ψ − iψ̄(∂/ −m)δψ = −iψ̄(−iǫaTa)(∂/ −m)ψ − iψ̄(∂/ −m)(iǫaTa)ψ = 0 , (4) where we used the trivial relation [Ta, γ ] = 0. (b) We use the so called Noether method (described in e.g. Di Francesco et al.: CFT Section 2.4.2) to...
متن کامل8.324 Relativististic Field Theory II, Assignment 3 Solution
implying C = 1 and δ (p) = δ (p̃). (b) Note that assuming p = ωp� dp� 1 dp � 2 2� � 0� (2π) 3 2ωp� f (p) = (2π) 3 δ p + m θ p f (p) d4p� � 2 2� � 0� = 3 δ p� + m θ p� f (p�) (2) (2π) dp � 2 2� � 0� dp� 1 = 3 δ p + m θ p f (p�) = 3 f (p�) (2π) (2π) 2ωp� In the second line we renamed p → p�, in the third we used | det Λ| = 1, p�2 = p and θ p�0 = θ p for Lorentz transformations connected to the ide...
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