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An approximate plan for the course is the following:

A. Solitons classical and quantum

1.  Simple examples in two dimensions. Small oscillations and stability. Particle-like solitons.
2. Topological Conservation Laws. Gauge theories revisited. Topological conservation laws and homotopy classes. Examples in two spatial dimensions. Examples in three spatial dimensions.
3. Abelian and non-abelian magnetic monopoles.
4. Quantum Solitons. Dashen Hasslacher and Neveu theory.
5. The sine-Gordon theory and teh Thirring model. 

B.     Instantons.

       1.  Instantons and bounces in particle Mechanics.

       2. The double well and instantons.

       3. The vaccum structure of gauge theories.

       4.  Yang-Mills  instantons.

       5. The abelian Higgs model in 1+1 dimensions.

       6.  The 't Hooft solution to the U(1) axial problem.

       7.   Instantons  in Quantum Chromodynamics.

        8. The fate of flase vacua.

C.    Basic Notions of topology.

        1. Homeomorphisms, homotopy and the notion of topological invariants.

        2. Manifolds and differential forms.

        3.  The fundamental group of a manifold. Simplexes and the triangulations of manifolds.

         4. Homology groups and eact sequences.

         5.  Higher homotopy groups and homotopy exact sequences.

         6.  Cohomology.

         7.   Morse theory.

          8. Defects, Textures and homotopy theory. 

General  Information

ΦΥΣ-801. Topology in Quantum Field Theory 

Hours: 4 ECTS: 6

Semester:  Fall

Teacher:  Elias Kiritsis

telephone: 2810 394209

e-mail: kiritsis@physics.uoc.gr

Lecture Hall:  @nd floor seminar room

Times of lectures:

Friday, 15:00-17:00

Office hours   :

Friday , 13:00-15:00

Office : 208

I would like to welcome you to the graduate advanced course on Topological Methods in Quantum Field Theory.

The course will be based on one  two-hour weekly meeting

and is a reading course .

Prerequisites in order to attend it are that you have passed (with a very good grade) an advanced quantum mechanics course and an Introductory Quantum Field Theory course.

 Otherwise you cannot manage this course, and I discourage you to take it for credit.      

The final grade will be determined by possible assignements and a final exam.

As it a reading course, each week, students will have a specific topic to read, and comprehead, and do all the required calculations.

There will be a weekly meeting with the instructor on Fridays where questions and problems of comprehension and calculation will be discussed.