Abstract:
The goal of this master-class is to outline the semiclassical
quantization of models of classical and quantum field theories
with gauge symmetry. The main examples will be the Yang-Mills
theory (its Euclidean version) in dimension 4 and the
Chern-Simons theory in dimension 3.
The class will start with the description of Lagrangian and Hamiltonian formulation of classical field theory. We will discuss the difference between first and second order classical field theories. Then we will see how the asymptotical expansion of oscillating integrals can be computed in terms of Feynman diagrams. After this we will move to the analysis of the semiclassical asymptotical expansions for the Yang-Mills theory and for the Chern-Simons theory. We will briefly discuss the renormalization issues for the Yang-Mills theory and will focus on invariants of 3-manifolds which appear as coefficients of the semiclassical expansion for the Chern-Simons theory. We will also see how the quantization of the Chern-Simons theory is related to the quantization of moduli spaces of flat connections in trivial principal G-bundles over surfaces.
The Master Class will follow, in parts, the Lecture Notes from the Holbaek Summer School on Quantum Gravity: http://staff.science.uva.nl/~nresheti/Holb-Quant-Gauge.pdf.
From Tuesday November 10 to Friday November 13 and from Tuesday November 17 to Friday November 20, 2009.
Preliminary schedule:
10:00-10:45 Lecture
10:45-11:15 Coffee break
11:15-12:00 Lecture
14:00-14:45 Lecture
14:45-15:15 Coffee break
15:15-16:00 Lecture
Location:
10 November: G3.1
11 November: Koll.G
12 November: G3.1 at 10:00-14:00 and G3.2 at 14:00-16:00
13 November: G3.1
17 November: Koll.G at 10:00-12:00 and Aud.G1 at 12:00-16:00
18 November: Koll.G
19 November: Koll.G at 10:00-12:00 and Aud.G2 at 12:00-16:00
20 November: G3.1
Organiser: Jørgen Ellegaard Andersen.
Revised 20.11.2009
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