Sirince school on mathematical and theoretical physics
27 August - 3 September, Nesin Mathematics Village, SIrince, Turkey
Basic
Applied methods of mathematical analysis: complex analysis, special functions
D. Diakonov
Gamma function
Zeta function
Fourier transform, Laplace transform and Mellin transform.
Completeness and orthogonality relations, Wronskian
Field quantization in curved space-time
Applied methods of mathematical analysis: integrals, differential equations
K. Bazarov
1. Сomplex integrals
2. Steepest descent method
3. Airy function
4. Spherical harmonics
5. Legandre functions
Introduction to General Relativity: Black Holes and Wormholes
P. Anempodistov
1. Point particle in curved spacetime. Tensor analysis. Equations of motion for a particle in curved spacetime.
2. Riemannian geometry.
3. Einstein-Hilbert action. Einstein equations, their linearization.
4. Solutions of Einstein equations. Black holes. Motion of particles in black hole background.
5. Wormhole solutions.
Gauge theory and solitons
E. Musaev
Dirac monopole
Scalar field theory in 1+1 dimensions, kink
Abrikosov vortex
BPS solitons and supersymmetry
Braneworld models
Advanced
Quantization methods
K. Gubarev
1. Setup of quantization problem. Canonical quantization.
2. Dirac approach to constrained systems.
3. Path integral quantization.
4. Deformation quantization.
5. Geometrical quantization.
Introduction to Supersymmetry
L. Astrakhantsev
1. Supersymmetry algebra
2. Superspace and Superfields I
3. Superspace and Superfields II
4. Wess-Zumino model
5. Sigma-model and Yang-Mills theories
Quantum effects in external fields
E. Akhmedov, A. Morozov
Klein effect
Schwinger effect from path integral instantons
Functional determinant in external electromagnetic field
4. Particle currents created by external fields (two lectures)
Student talks
V. Lapushkin, Quantum effects in external fields
V. Novoseltsev, Instantons in double well potentials