Dr habil. Christian Jäkel
Overview
Position:
Senior Lecturer
Email:
JaekelCD@cardiff.ac.ukTelephone: +44(0)29 208 70617
Fax: +44(0)29 208 74199
Extension: 70617
Location: M/2.44
Research Interests
My main research area is mathematical physics, especially mathematical aspects of quantum field theory and statistical mechanics. My early work concentrated on non-relativistic Fermions with (a large class of) pair-interactions, both in and out of equilibrium. In the sequel I turned to relativistic field theory, working in an operator algebraic setting and concentrating on structural aspects like statistical dependence of measurements in spatially separated regions, cluster theorems, phase-space properties encoded in inclusions of operator algebras, and the construction of a quantum field theory at arbitrary temperature if it is given at a fixed temperature. Currently I am working in constructive quantum field theory, lastly on curved space-times. Future work will concentrate on non-equilibrium statistical mechanics.
Research Group
Analysis and Differential Equations
Recent Significant Publications
Jäkel C D, with A. Jaffe and R. Martinez., Complex Classical Fields: A Framework, 30 p., see also http://arxiv.org/abs/1201.6003.
Jäkel C D, and Robl, F., The relativistic KMS condition for the thermal n-point functions of the P(\phi)_2 model, to appear in Commun. Math. Phys., see also http://arxiv.org/abs/1103.3609
Jäkel C D, and Robl, F., The Hölder Inequality for KMS States, to appear in Lett. Math. Phys., see also http://arxiv.org/abs/1103.3608
Jäkel C D, and Wreszinski, W.F., A Goldstone theorem in thermal relativistic quantum field theory, J. Math. Phys. 52, 012302 (2011);
Jäkel C D, Narnhofer H and Wreszinski W F, On the mixing properties for a class of states of relativistic quantum fields, J. Math. Phys. 51/4 (2010).
Teaching
MA3003 Groups, Rings and Fields
MA0213 Group Theory (Winter term 2007)
MA0212 Linear Algebra (Summer term 2007)
Operator Algebras (Winter term 2006)
Quantum Statistical Mechanics (Summer term 2001)
General Relativity (Summer term 2001)
Mathematics for Physicists (Part III, Winter term 2000)
Mathematics for Physicists (Part I, Summer term 2000)
Mathematics for Physicists (Part III, Winter term 1999)
Administrative Duties
Member of School Mathematics Subject Panel
Member of Board of Studies
Responsible (together with Stefan Hollands) for the administration of Final Year Projects
Erasmus activities coordinator (together with Stefan Hollands)
Publications
Peer-Reviewed Publications
Complex Classical Fields: A Framework , with A. Jaffe and R. Martinez, 30 p., see also http://arxiv.org/abs/1201.6003.
Jäkel C D, and Robl, F., The relativistic KMS condition for the thermal n-point functions of the P(\phi)_2 model, to appear in Commun. Math. Phys., see
also http://arxiv.org/abs/1103.3609
Jäkel C D, and Robl, F., The Hölder Inequality for KMS States, to appear in Lett. Math. Phys, see also http://arxiv.org/abs/1103.3608
Jäkel C D, and Wreszinski, W.F., A Goldstone theorem in thermal relativistic quantum field theory,
J. Math. Phys. 52, 012302 (2011);
Jäkel C D, Narnhofer H and Wreszinski W F, On the mixing properties for a class of states of relativistic quantum fields,
J. Math. Phys. 51/4 (2010).
Stability and Related Properties of Vacua and Ground, with W. Wreszinski, Ann. Phys. 323, 251-266 (2008)
On the relativistic KMS condition for the P(\phi)_2 model, with C. Gérard, Prog. Math. 251, 125-140 (2007)
An Exchange Identity for Non-linear Fields, with A. Jaffe, Commun. Math.Phys. 264, 283-289 (2006)
Thermal quantum fields without cutoffs in 1+1 space-time dimensions, with C. Gérard, Rev. Math. Phys. 17, 113-173 (2005)
Thermal quantum fields with spatially cutoff interactions in 1+1 space-time dimensions, with C. Gérard, J. Funct. Anal. 220, 157-213 (2005)
The relation between KMS states for different temperatures, Ann. H. Poincaré 5, 1-30 (2004)
The Reeh-Schlieder property for ground states, Ann. Phys. (Leipzig) 12, 289-299 (2003)
Some comments on entanglement and local thermofield theory, Foundations of Physics Lett. 14, 1-16 (2001)
The Reeh-Schlieder property for thermal field theories, J. Math.Phys. 41, 1745-1754 (2000)
Two algebraic properties of thermal quantum field theories, J. Math.Phys. 40, 6234-6244 (1999)
Decay of spatial correlations in thermal states, Ann. l'Inst. H.Poincaré 69, 425-440 (1998)
On the uniqueness of the equilibrium state for an interacting Fermion gas at high temperatures and low densities, Lett. Math. Phys. 33, 87-97 (1995)
Galilei invariant molecular dynamics, with G. Hörmann, Publ. RIMS 31, 805-827 (1995)
Asymptotic triviality of the Mĝller operators in Galilei invariant quantum field theories, Lett. Math. Phys. 21, 343-350 (1991)
Encyclopedia of Mathematical Physics
Chapter: Thermal QFT (MS number: 89), Encyclopedia of Mathematical Physics, Elsevier, accepted for publication, to be published in 2006.
Theses
Asymptotic Triviality of Møller Operators, Diplomarbeit, Universität Wien (1991)
Uniqueness of the KMS State for Interacting Fermions, Dissertation, Universität
Wien (1993)
Mathematical Foundations of Thermal Field Theory, Habilitationschrift, LMU München (2004)
Research
Current and Past Collaborators
Joao Barrata , Universidade de Sao Paulo, Brazil
Jürg Fröhlich, ETH Zurich, Switzerland
Christian Gerard , Universite Paris XI (Orsay), France
Günther Hörmann, University Vienna, Austria
Arthur Jaffe , Harvard University
Jens Mund , Juiz de Fora, Brazil
Heide Narnhofer, University Vienna, Austria
Florian Robl, Cardiff University, Wales
Rainer Verch, University Leipzig, Germany
Urs Wiedemann, CERN, Switzerland
Walter Wreszinski, Universidade de Sao Paulo, Brazil
External Funding Since 2000
Leverhulme research grant, "Particle Aspects of Thermal Quantum Fields", Duration: three years, starting April 1, 2009, funded by the Leverhulme Trust.
CONDECYT research network grant between the University of Talca, Chile, and the Operator Algebra Research Group in Italy, approved in November 2007
Fondecyt international visitors research grant (Chile), approved June 2007 .
Fondecyt visitors research grant (Chile), approved March 2007 (this is a four years grant, but it will be prematurely terminated in March 2008).
Visiting Professorship, Univ. de Sao Paulo, awarded by FAPESP (2004-2005)
Marie Curie Individual Fellowship, awarded by the EC (2001-2003)
Major Conference Talks Since 2004
Rigorous QFT in the LHC era, Workshop at the Erwin Schrödinger Institute (ESI), Vienna, Austria, September 20 to October 1, 2011. (together with Christoph Kopper (Ecole Ploytechnique, Palaiseau) and Gandalf Lechner (University of Vienna).
Dynamics of infinite quantum systems, Workshop at the Erwin Schrödinger Institute (ESI), Vienna, Austria, June 1-14, 2009.
"Interacting Quantum Fields on de Sitter space" talk given on joint work with Joao Barata and Jens Mund, XVII Congreso de Matematica Capricornio COMCA 2007, Copiapo, Chile, August 2007;
"Interacting Quantum Fields on de Sitter space" talk given on joint work with Joao Barata and Jens Mund, Conference "Topics in Mathematical Physics", Sao Paulo, Brazil, August 2006;
"The relativistic KMS condition", talk given on joint work with Christian Gerard, Brazilian Operator Conference, Florianopolis, Brazil, July 2006;
"Interacting Quantum Fields on de Sitter space" talk given on joint work with Joao Barata and Jens Mund, Workshop on "Complex Quantum and Classical Systems and Effective Equations", Erwin Schrödinger Institute (ESI), Vienna, Austria, June 2006
Research Visits Since 2004
Harvard University, USA, January 2012
Aarhus University, Denmark, December 2011
Erwin Schrödinger Institut, Vienna, Austria, September 2011
Harvard University, Cambridge, USA, April 2010.
Erwin Schrödinger Institute, Vienna, Austria, July 2009.
Swiss Federal Institute of Technology (ETH Zurich), May 2009.
University of Sao Paulo, Brazil, Dezember 2009 to January 2010.
September 2008: Erwin Schrödinger Institute, Vienna, Austria
May 2008: IHES, Bures-sur-Yvette, France
April 2008: Universidade de Sao Paulo, Brazil
Feb.-March 2008: Harvard University, Cambridge, USA
Dec. 2006-Feb. 2007: IHES, Bures-sur-Yvette, France
June 2006: Erwin Schrödinger Institute, Vienna, Austria
Oct.-Dec. 2005: ETH Zurich, Switzerland
September 2005: Centre de Physique Théorique, Marseille, France
February 2005: Harvard University, Cambridge, USA
March 2005: Erwin Schrödinger Institute, Vienna, Austria
April-July 2004: ETH Zurich, Switzerland
Postgraduate Students
Ph.D. Students
Dr. Florian Robl, Thesis: Relativistic quantum field theory at positive temperature, April 25, 2012.
Final Year project students
Ross McKenzie, Project title: Unstable Manifolds (2012)
Magarete Levi, Project title: Foundations of Modern Analysis, since October 1, 2010
Heledd Iorwerth, Project title: Dynamical Systems, Cardiff University, School of Mathematics (2010)
Sian Halcrow, Project title: Dynamical Systems and Hopf Bifurcation, Cardiff University, School of Mathematics (2009).
Geoffrey Jones, Project title: Divergent series and Borel Summation, Cardiff University, School of Mathematics (2009).
Biography
Msc - University of California at Davis, USA 1989
Mag. rer. nat. - University of Vienna, Austria 1991, Adviser: Prof. W. Thirring
PhD - University of Vienna, Austria 1993, Adviser: Prof. Walter Thirring
Habilitation - LMU Munich, Germany 2004
Previous Positions
2007-2009 Lecturer, School of Mathematics, Cardiff University
2006-2007 Associate Professor, Universidad Talca, Chile
2004-2005 Visiting Professor, Universidade de Sao Paulo, Brazil
2003-2004 Researcher (BAT Ib), LMU Munich, Germany
2001-2003 EC-Marie Curie Individual Fellowship, École Polytechnique, Palaiseau, France
1999-2001 Assistant Professor (Vertrags-Ass.), Theor. Physics, Univ. Innsbruck, Austria
1998-1999 Postdoctoral fellow, TMR-network Operator Algebras and Non Commutative Geometry, Universita di Roma Tor Vergata, Italy
1995-1998 Postdoctoral fellow, University of Vienna, Austria
1993-1995 Erwin Schrödinger fellow of the Austrian Academy of Science, University of Hamburg, Germany