Lectures at the First Erlangen Fall School on Quantum Geometry

Recorded Lectures

All lectures held at the First Erlangen Fall School on Quantum Geometry were recorded and are available in different viedo formats. The vidoes can be watched under the following link: Recorded lectures

Lecture Notes

The slides of Prof. Tudor Ratiu lectures can be downloaded as a pdf file from here.

Additional References

Group-valued moment maps

Alekseev, A., A. Malkin, and E. Meinrenken,
Lie group valued moment maps,
J. Differential Geom. 48:3 (1998), 445-495

Meinrenken, E.,
Lectures on pure spinors and moment maps,
in Poisson geometry in mathematics and physics, 199-222, Contemp. Math., 450, Amer. Math. Soc., Providence, RI, 2008

Anton Alekseev, Eckhard Meinrenken, Chris Woodward,
Duistermaat-Heckman distributions for group valued moment maps,
Geom. Funct. Anal. 12 (2002), 1-31

Infinite dimensional Poisson Geometry

Beltita, D., T. S. Ratiu, and B. Tumpach,
The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits,
J. Funct. Anal. 247:1 (2007), 138-168

Gay-Balmaz, F., and T. Ratiu,
Affine Lie-Poisson reduction, Yang-Mills magnetohydrodynamics, and superfluids,
J. Phys. A 41 (2008), no. 34, 344007, 24 pp

Odzijewicz, A., and T. Ratiu,
Induced and coinduced Banach Lie-Poisson spaces and integrability,
J. Funct. Anal. 255:5 (2008), 1225-1272

Odzijewicz, A., and T. Ratiu,
Induction for weak symplectic Banach manifolds,
J. Geom. Phys. 58:6 (2008), 701-719

QFT on curved spacetimes

R. Brunetti, K. Fredenhagen and P.L. Ribeiro,
Algebraic Structure of Classical Field Theory I: Kinematics and Linearized Dynamics for Real Scalar Fields,
arXiv:1209.2148 [math-ph].

C. Bar, (ed.) and K. Fredenhagen, (ed.), Quantum field theory on curved spacetimes,
Lect. Notes Phys. 786 (2009) 1.

Further lecture notes (some in German only) can be found here .

Loop quantum gravity

A. Ashtekar and J. Lewandowski,
Background independent quantum gravity: A Status report,
Class. Quant. Grav. 21 (2004) R53 [gr-qc/0404018].

T. Thiemann,
Modern canonical quantum general relativity,
Cambridge, UK: Cambridge Univ. Pr. (2007) 819 p

K. Giesel and H. Sahlmann,
From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity,
PoS QGQGS 2011 (2011) 002 [arXiv:1203.2733 [gr-qc]].

Infinite dimensional Poisson geometry

Beltita, D., T. S. Ratiu, and B. Tumpach,
The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits,
J. Funct. Anal. 247:1 (2007), 138-168

Gay-Balmaz, F., and T. Ratiu,
Affine Lie-Poisson reduction, Yang-Mills magnetohydrodynamics, and superfluids,
J. Phys. A 41 (2008), no. 34, 344007, 24 pp

Odzijewicz, A., and T. Ratiu,
Induced and coinduced Banach Lie-Poisson spaces and integrability,
J. Funct. Anal. 255:5 (2008), 1225-1272

Odzijewicz, A., and T. Ratiu,
Induction for weak symplectic Banach manifolds,
J. Geom. Phys. 58:6 (2008), 701-719