Wahlpflichtvorlesung für
So.Se. 2013:
“Topological Objects in (Quantum) Field Theory”
von
Priv. Doz. Dr. Francesco Giacosa
Zeit (Time) (2 Std) Fr, 12:00
(c.t.)14:00, wöchentlich (weekly).
Erster Termin (first lecture):
19/4/2013.
Raum (Room): 2.114 (AquariumRaum)
Webpage: http://th.physik.unifrankfurt.de/~giacosa/topobj.html
Email: giacosa@th.physik.unifrankfurt.de
The goal of the lecture is to
describe some examples of topological objects: these are highly interesting and
nontrivial solutions of nonlinear field theories. Such solutions can be
compared to huge and stable waves. Lower dimensional field theories represent a
good starting point due to their simplicity and the possibility to visualize
some topological stable configurations. The related concept of instantons is
also introduced in this context. Its role for quantum mechanics is explained
with simple examples.
Then, the attention is driven
to fourdimensional field theories. In the framework of electrodynamics the
monopole is described. The rich topological structure of YangMills theory in
four dimensions is addressed: the role of monopoles and instantons in
YangMills theory and, more in general, in QCD, is discussed.
Other interesting topological
objects, such as the Skyrmion and the sphaleron, will be presented.
Themes
Book on topology: R. Rajamran, Solitons
and Instatnons
Lecture on topology: G. ‘t Hooft, Monopoles, Instantons, and
confinement”. http://arxiv.org/pdf/hepth/0010225v1.pdf
Handsout

Introduction of the
course (Fr. 19/4): pdf.

Field theory in 1+1
dim, wavepacket spreading, the kink as a easy soliton (Fr. 26/4): pdf.

The kink, part 2.
Energy, Topological charge and current (Fr. 10/5): pdf.
(Links: http://en.wikipedia.org/wiki/Soliton ; Video: https://www.youtube.com/watch?v=wEbYELtGZwI&list=PLKTMChjaq_EMzMJ3lIrTvrlT2fI1Rou4E&index=1)

SineGordon model. Derrik’s theorem
(Fr. 17/5): pdf. (Link with animations of the sineGordon mode lhttp://en.wikipedia.org/wiki/Sine%E2%80%93Gordon_equation)

SineGordon (part II,
24/5/2013): scattering and bound state: pdf.
Instanton in 1+0 dimensions and discussion of solitons/instantons: pdf.

Soliton/instanton (part II,
31/5/2013): pdf. Solitions in the
O(3) model in 1+2 dimensions: pdf.

The nonlinear O(3) model in 1+1
dimensions (14/6/2013): pdf. The vortex solution in 1+2
dimensions with a U(1) photon field: pdf.

The AharonovBohm effect (21/6/2013): pdf. The Dirac magnetic monopole: pdf.

The Dirac magnetic monopole (part 2,
5/7/2013): pdf. The
dualsuperconductivity picture of confinement: pdf

‘t HofftPolyakov Monopole in the
GeorgiGlashow model and the dyon in SU(2) YangMills (12/7/2013): pdf.

Recall of the SU(N) YangMills
theory and the phenomenon of dimensional transmutation (12/7/2013): pdf.

Instatons in SU(2)YangMills
and their role in QCD (19/7/2013): pdf.
Next
lectures with student’s presentations:
Wednesday
21/8/2013 at 14:00 in room 2.114. (Subject of my presentationlecture: the
Polyakov loop: pdf).
Wednesday
18/9/2013 at 14:00 in room 2.114. (Subject of my presentationlecture: the
Skyrmion).
Remember to send me an Email with the choice of your chosen topic.
Firstcome first serve...
Contact: giacosa@th.physik.unifrankfurt.de