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- Florian Conrady

Spacetime represents one of the remaining frontiers in

theoretical physics. We have successful theories of fields /in/

spacetime and of the geometry /of/ spacetime. But there is no

established theory of spacetime itself, a theory that would

explain why we live in a spacetime and not in something

completely different.

My research contributes to attempts to find such a theory. So

far I have mostly worked on loop quantum gravity and spin foam

models, but I am also open to various other approaches such as

noncommutative geometry, causal sets, quantum graphity and

matrix models. All these research directions have in common

that they aim to explain spacetime manifolds in terms of more

fundamental objects. They try to produce space from no space.

Loop quantum gravity and spin foam models are theories whose

quanta (or particles) are given by elementary pieces of

spacetime such as triangles and tetrahedra. It is hoped that

spacetime as a whole arises through the interaction of many of

these quanta. Whether this is indeed the case is an open

question and often referred to as the problem of the

semiclassical limit.

In joint work with Laurent Freidel, I have investigated this

semiclassical limit and shown that spin foam models reduce to a

certain form of Regge calculus, another formulation of quantum

spacetime. This reduction is an important consistency check; if

it failed, the theory would not have the degrees of freedom of

gravity.

Another of my projects concerned the signature and causal

structure in spin foam models. Previously spin foam models were

exclusively defined with spacelike triangles, and it was not

known how to implement timelike triangles. This is a problem,

since it means that all edges of discrete spacetime are

spacelike and it is not clear how to couple matter particles to

it (which have timelike worldlines). In work together with the

Master's student Jeff Hnybida, I have shown how the inclusion

of timelike triangles can be achieved and an associated

extended model of spin foams was defined. Remarkably, the area

of timelike surfaces is quantized in a similar way as for

spacelike surfaces.

Recently I finished work on a model of quantum graphity that

gives a successful example of the 'space from no space' idea.

It is a statistical model of graphs in which 2-dimensional

spaces arise as ground states.

- 2005 - 2007 Institute for Gravitational Physics and Geometry, Penn State University postdoctoral fellow

- 1-year scholarship, DAAD, ~14000 Euro
- 2-year scholarship, Daimler Benz Foundation, ~28000 Euro

- Florian Conrady, Space as a low-temperature regime of graphs, J.Statist.Phys.142:898, February 2011, arXiv: 1009.3195
- Florian Conrady, Jeff Hnybida, Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases, J.Math.Phys. 52:012501, January 2011, arXiv: 1007.0937
- F.Conrady, J.Hnybida, A spin foam model for general Lorentzian 4-geometries, Class.Quant.Grav.27, 185011, July 2010, arXiv: 1002.1959 [gr-qc]
- F.Conrady, Spin foams with timelike surfaces, Class.Quant.Grav.27, 155014, June 2010, arXiv: 1003.5652 [gr-qc]
- F.Conrady, L.Freidel, Quantum geometry from phase space reduction, J.Math.Phys. 50, 123510 (2009), arXiv: 0902.0351 [gr-qc].
- F.Conrady, L.Freidel, Path integral representation of spin foam models of 4d gravity, Class.Quant.Grav. 25, 245010, December 2008, 32 pages, arXiv: 0806.4640 [gr-qc]
- F.Conrady, L.Freidel, Semiclassical limit of 4d spin foam models, Phys.Rev. D78, 104023, November 2008, 18 pages, arXiv: 0809.2280 [gr-qc]
- F.Conrady, Free vacuum for loop quantum gravity, Class.Quant.Grav. 22, No.16, July 2005, 3261--3293, arXiv: gr-qc/0409036
- F.Conrady, C.Rovelli, Generalized Schrodinger equation in Euclidean field theory, Int.J.Mod.Phys. A19, No.24, September 2004, 4037--4068, arXiv: hep-th/0310246
- F.Conrady, L.Doplicher, R.Oeckl, C.Rovelli, M.Testa, Minkowski vacuum in background independent quantum gravity}, Phys.Rev. D69, 064019, March 2004, 7 pages, arXiv: gr-qc/0307118
- F.Conrady, C.Schweigert, Topologization of chiral representations, Commun.Math.Phys. 245, March 2004, 429--448, arXiv: hep-th/0210215
- F.Conrady, Space as a low-temperature regime of graphs, arXiv: 1009.3195 [gr-qc]
- F.Conrady, J.Hnybida, Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases, July 2010, arXiv: 1007.0937 [gr-qc]
- F.Conrady, Igor Khavkine, An exact string representation of 3d SU(2) lattice Yang-Mills theory}, arXiv: 0706.3423 [hep-th]
- F.Conrady, Dual representation of Polyakov loop in 3d SU(2) lattice Yang-Mills theory}, arXiv: 0706.3422 [hep-lat]
- F.Conrady, Analytic derivation of gluons and monopoles from SU(2) lattice Yang-Mills theory, I. BF Yang-Mills representation, arXiv: hep-th/0610236
- F.Conrady, Analytic derivation of gluons and monopoles from SU(2) lattice Yang-Mills theory, III. Plaquette representation, arXiv: hep-th/0610238
- F.Conrady, Analytic derivation of gluons and monopoles from SU(2) lattice Yang-Mills theory, II. Spin foam representation, arXiv: hep-th/0610237
- F.Conrady, Geometric spin foams, Yang-Mills theory and background-independent models, arXiv: gr-qc/0504059
- F.Conrady, Science fiction of everything, in "Are we there yet? The search for a theory of everything", edited by M.Emam, Bentham Science Publishers, April 2011.

- Space as a low-temperature regime of graphs, seminar AEI Potsdam
- Space as a low-temperature regime of graphs, seminar CPT Marseille
- A spin foam model for general Lorentzian 4-geometries, Open Problems in Loop Quantum Gravity, Zakopane (invited)
- Quantum geometry from phase space reduction, seminar Penn State University (invited)
- Spin foam models and the transition from first-order to second-order gravity, Loops 09, Beijing
- Simplicial complexes from condensation, Emergent Gravity IV, Vancouver
- Spin foam models and the transition from first-order to second-order gravity, 12th Marcel Grossmann meeting, Paris
- Loop quantum gravity and spin foam models - Recent progress and open problems, Theory Canada 5, Fredericton (invited)
- Loop quantum gravity and spin foam models - Recent progress and open problems, seminar LPT Orsay
- Quantum geometry from phase space reduction, seminar CPT Marseille
- Semiclassical analysis of spin foam models of 4d gravity, Quantum Geometry and Quantum Gravity, Nottingham
- Spin foams, gauge-string duality and renormalization, Loops 07, Morelia
- Spin foams, monopoles and confinement, seminar CPT Marseille
- Spin foams, monopoles and confinement, seminar ITF Utrecht
- Spin foams, monopoles and confinement, seminar MPI Potsdam
- Gluon propagator from Yang-Mills spin foams, Quantum Gravity in the Americas III, Penn State University
- String representation of lattice gauge theory and spin foam models, seminar Institute of Theoretical Physics Heidelberg
- String representation of lattice gauge theory and spin foam models, Loops 05, MPI Potsdam
- Free vacuum for loop quantum gravity, seminar Penn State University
- PIRSA:10040039, Spin foams with timelike surfaces, 2010-04-06, International Loop Quantum Gravity Seminar
- Lorentzian spin foams, 2010-02-11, QG group meeting
- Quantum geometry from phase space reduction, 2009-02-26, QG group meeting
- PIRSA:06110001, Spin foams, monopoles and confinement, 2006-11-02, Quantum Gravity
- PIRSA:04100027, Vacuum State for LQG, 2004-10-29, Workshop on Quantum Gravity in the Americas: Status and future directions

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