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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