UMCP Department of Mathematics

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24 Οκτ 2013 (πριν από 3 χρόνια και 5 μήνες)

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MATH 648M:
Advanced Analytic Methods with Applications

Instructor:

Prof. Dio Margetis (
dio@math.umd.edu
, x 5
-
5455)

TuTh

9:30
-
10:45am,
Rm

Math 0411

Website:

www.math.umd.edu/~dio/courses/648M

FIG. 2:
Electron
-
electron elastic scattering

in quantum electrodynamics: What is the
total scattering cross section in the limit of
high energy?

FIG. 1:

Temperature around a plate (red:
hot, to blue: cold). This can be derived by
solving a singular integral eqn.

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.

Lagrangian formulation: action principle; symmetries.

Perturbation theory: Born
-
Neumann series and extensions.

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;

analytical properties; high
-
energy asymptotics.

.

UMCP Department of Mathematics

This

Spring

the Math Department offers the graduate course…

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