Quantum Field Theory - Mathematical Tripos - Final Exam, Exams of Mathematics

Download Quantum Field Theory - Mathematical Tripos - Final Exam and more Exams Mathematics in PDF only on Docsity! MATHEMATICAL TRIPOS Part III Thursday, 27 May, 2010 9:00 am to 12:00 pm PAPER 42 QUANTUM FIELD THEORY Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight. STATIONERY REQUIREMENTS SPECIAL REQUIREMENTS Cover sheet None Treasury Tag Script paper You may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator. 2 1 The Klein-Gordon field φ(x) has mode expansion φ(x) = ∫ d3p (2π)3 1 √ 2Ep (ape −ip.x + a† p eip.x) , where p = (p0,p). In the interaction picture explain what is meant by the time ordered product; the normal ordered product; the Feynman propagator. State and prove Wick’s theorem and explain how the above quantities are related. Outline how you would derive the Feynman rules for correlation functions 〈 0|T (φ(x1), φ(x2) . . . φ(xn))S|0 〉 , where S is the S-matrix in the theory with Lagrange density L = 1 2 ∂µ φ∂ µ φ − 1 2 m2 φ2 − λ 4! φ4 . Part III, Paper 42