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**Time: ** 9. December 2011, 11:00h

**Place: ** Institute of Physics, room 300

**Speaker: ** Dimitar Mladenov

**Title: ** Integrable many-body systems and Bianchi cosmological models

**Abstract:**

It is shown that the geodesic motion on the GL(n,R) group manifold endowed with a bi-invariant metric corresponds to a generalizations of the n-particle Calogero-Moser-Sutherland model and the non-periodic Toda chain. Using the methods of Hamiltonian reduction these many-body systems are related to Bianchi cosmological models.

**Time: ** 23. September 2011, 11:00h

**Place: ** Institute of Physics, room 300

**Speaker: ** Marko Vojinovic

**Title: ** Poincare 2-group and new action for general relativity

**Abstract:**

We shall introduce the concept of a 2-group, specifically the Poincare 2-group. Then we shall construct the topological BFCG action and demonstrate how it can be constrained to give general relativity. A short analysis of the equations of motion will be given, as well as the extension of the formalism to include matter fields. Finally, we shall briefly discuss the procedure of spinfoam quantization of the model.

**Time: ** 3. June 2011, 11:00h

**Place: ** Institute of Physics, room 300

**Speaker: ** Igor Salom

**Title: ** Generalization of the Gell-Mann decontraction formula for sl(n,R) algebras (part 2)

**Abstract:**

The so-called Gell-Mann (decontraction) formula is an expression for the transformation constructed to be inverse to the Inonu-Wigner contraction. Actually, it is a prescription, since the formula does not hold for all Lie algebras and their representations. In the situations where the formula is valid, it is enormously important because it effectively gives expressions for the representations of the algebra operators, in a physically convenient basis. For the case of sl(n,R) algebras we shall show what is the validity domain of this formula and we shall demonstrate that it can be generalized in such a way so that it is valid for all representations. As an immediate application of the formula we shall derive a closed form expression for the matrix elements of sl(n,R) operators in an arbitrary representation.

**Time: ** 27. May 2011, 11:00h

**Place: ** Institute of Physics, room 300

**Speaker: ** Igor Salom

**Title: ** Generalization of the Gell-Mann decontraction formula for sl(n,R) algebras (part 1)

**Abstract:**

The so-called Gell-Mann (decontraction) formula is an expression for the transformation constructed to be inverse to the Inonu-Wigner contraction. Actually, it is a prescription, since the formula does not hold for all Lie algebras and their representations. In the situations where the formula is valid, it is enormously important because it effectively gives expressions for the representations of the algebra operators, in a physically convenient basis. For the case of sl(n,R) algebras we shall show what is the validity domain of this formula and we shall demonstrate that it can be generalized in such a way so that it is valid for all representations. As an immediate application of the formula we shall derive a closed form expression for the matrix elements of sl(n,R) operators in an arbitrary representation.

**Time: ** 29. April 2011, 11:00h

**Place: ** Institute of Physics, room 300

**Speaker: ** Nenad Manojlovic

**Title: ** Jordanian deformation of the open XXX-spin chain

**Abstract:**

We find the general solution of the reflection equation associated with the Jordanian deformation of the $SL(2)$-invariant Yang R-matrix. The special scaling limit of the XXZ model with general boundary conditions leads to the same K-matrix. Following the Sklyanin formalism, we derive the Hamiltonian with the boundary terms in explicit form. We also discuss the structure of the spectrum of the deformed XXX model and its dependence on the boundary conditions.

**Time: ** 27. April 2011, 11:00h

**Place: ** Institute of Physics, room 300

**Speaker: ** Marko Vojinovic

**Title: ** Introduction to Loop Quantum Gravity (3/3)

**Abstract:**

This is the third seminar in the 3-lecture course on Loop Quantum Gravity. We shall demonstrate the basics of the covariant nonperturbative quantization of the gravitational field, i.e. the spinfoam formalism. The relationship between general relativity and the topological BF theory will be established, and we shall define the discretized path integral for the BF theory. This will then be modified to accomodate for the simplicity constraints which reduce BF theory to general relativity. The lectures are mainly intended for graduate students, so the technical level will not be high and should be suitable for everyone interested.

**Time: ** 20. April 2011, 12:00h

**Place: ** Institute of Physics, room 300

**Speaker: ** Marko Vojinovic

**Title: ** Introduction to Loop Quantum Gravity (2b/3)

**Abstract:**

This is the continuation of the second lecture of the 3-lecture course on Loop Quantum Gravity. We shall demonstrate how spin network states arise in the theory, and what are their main properties. Then we shall pass on to the area and volume operators, and discuss their spectrum. The lectures are mainly intended for graduate students, so the technical level will not be high and should be suitable for everyone interested.

**Time: ** 15. April 2011, 11:00h

**Place: ** Institute of Physics, room 300

**Speaker: ** Marko Vojinovic

**Title: ** Introduction to Loop Quantum Gravity (2a/3)

**Abstract:**

This is the second seminar in the 3-lecture course on Loop Quantum Gravity. We shall demonstrate the procedure of nonperturbative canonical quantization of general relativity in the Schroedinger picture. The main topics to be reviewed are the classical and quantum constraints, definition and separability of the Hilbert space, loop transform and spin network basis. Finally, we shall discuss the area and volume operators and their spectra, as an introduction to the spinfoam formalism (third lecture). The lectures are mainly intended for graduate students, so the technical level will not be high and should be suitable for everyone interested.

**Time: ** 8. April 2011, 11:00h

**Place: ** Institute of Physics, room 300

**Speaker: ** Marko Vojinovic

**Title: ** Introduction to Loop Quantum Gravity (1/3)

**Abstract:**

This is a first seminar in the 3-lecture course on Loop Quantum Gravity. We shall begin with the formulation of the problem of quantization of the gravitational field, discuss the main issues, various approaches to QG, and mention their main features and drawbacks. Then we shall focus attention on LQG approach and discuss the properties of the classical LQG action, before going into the details of the canonical quantization (second lecture) and covariant quantization (third lecture). The lectures are mainly intended for graduate students, so the technical level will not be high and should be suitable for everyone interested.

**Time: ** 1. April 2011, 11:00h

**Place: ** Institute of Physics, room 300

**Speaker: ** Maja Buric

**Title: ** On the renormalizability of noncommutative electrodynamics in curved spacetime

**Abstract:**

We will define the U(1) gauge-model in curved noncommutative space and then examine the divergencess of the tadpole diagrams.

**Seminars for the year:**
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007