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Transcript
This Spring the Math Department offers the graduate course… MATH 648M: Advanced Analytic Methods with Applications TuTh 9:30-10:45am, Rm Math 0411 Website: www.math.umd.edu/~dio/courses/648M Instructor: Prof. Dio Margetis ([email protected], x 5-5455) FOCUS: Mathematical concepts and analytical tools used in classical mechanics as well as quantum mechanics and quantum field theories. Applications from: fluid mechanics, elasticity, electromagnetism, atomic and particle physics. TOPICS: PART I: Green’s functions and boundary value problems in classical mechanics. Integral equations: Fredholm eqns; the Wiener-Hopf technique. FIG. 1: Temperature around a plate (red: Lagrangian formulation: action principle; symmetries. hot, to blue: cold). This can be derived by solving a singular integral eqn. Perturbation theory: Born-Neumann series and extensions. e- e- PART II: Mathematical elements of quantum mechanics. Quantum fields: Basic notions; canonical quantization; invariance properties and gauge transformations; Yang-Mills gauge field theories. Calculus of Feynman diagrams: The S-matrix; divergencies; eeanalytical properties; high-energy asymptotics. FIG. 2: Electron-electron elastic scattering in quantum electrodynamics: What is the . total scattering cross section in the limit of high energy? UMCP Department of Mathematics
