Mathematical Physics GroupQuantum field theory and Gravitation 
Institute for Theoretical Physics, University of Göttingen





















Alumni Guests  Addresses 
Publications Diploma and PhD Theses Research Reports 
Local Quantum
Physics Crossroads Mathematics Institute Göttingen EU Network Noncommutative Geometry AQFT  50 years 
Studies of fundamental questions of physics by methods of mathematical physics have a tradition of long standing in Göttingen. In the sixties, G. Lüders and H.J. Borchers established mathematically oriented quantum field theory and statistical mechanics at the Institute of Theoretical Physics; many papers from Göttingen had great influence in these fields lying at the interface of local quantum physics and functional analysis.
Research along these lines is continued. The focus is on central questions concerning the construction as well as the interpretation of relativistic quantum field theories which cannot be answered by conventional (perturbation or numerical) methods; a complementary approach will  hopefully  lead to a deepened structural understanding of the theory.
The group's projects can be subdivided into five domains:
Further details:
(1) Constructive aspects
A novel approach for the analysis of quantum field theories is based on
an advanced TomitaTakesaki theory, which has been initiated by H.J.
Borchers and H.W. Wiesbrock. It could be demonstrated that the knowledge
of a few subalgebras of the observable algebra suffices to characterize
and reconstruct the global theory. A further study of these subalgebras
might lead to a new class of invariants, and open new ways of
classification and construction of theories. Furthermore, the method is
apt to define vacuumlike states in curved spacetimes by a condition of
geometric modular action as proposed by D. Buchholz and S. J.
Summers. Work on these questions, which are important for the analysis and
construction of quantum field theories, is being continued. (H.J.
Borchers, D. Buchholz)
The implications of conformal symmetry for the kinematical and dynamical structure is analyzed. In two dimensions, an abundance of theories has been constructed, apt to test and to extend the general theory of superselection sectors and statistics. Algebraic methods of construction arise from the application of subfactor theory. These allow for the classification of "boundary CFTs" on a halfspace. (K.H. Rehren) In four dimensions, the restrictivity of the assumption of global conformal invariance is studied, using operator product expansions and partial wave expansions. (K.H. Rehren, I.T. Todorov)
(2) Symmetries and particles
In view of the quantum equivalence of certain (gauge) theories which are
classically distinct theories it may be asked whether the standard
interpretation (with the help of gauge theories) of the inner structure
of hadronic matter (quarks, gluons, colour) is free of arbitrariness. In order
to analyse this problem D. Buchholz and R. Verch established a new method to
determine the short distance structure of local observables in quantum field
theory (scaling limit). Based on this method a procedure is being developed
to determine the symmetry group and the particle content of a theory
at small length scales directly from the observables  and thus free of
arbitrariness. (D. Buchholz, M. Lutz, R. Verch)
Because of infrared effects the superselection structure of theories with abelian gauge symmetries and corresponding free (electric and magnetic) charges is rather complicated; their particle content and their energymomentum spectrum cannot be described by the particle notion of Wigner. The spectrum can be analysed by methods of complex analysis developed by H.J. Borchers; D. Buchholz introduced the notions of charge class and particle weight for the sector analysis. With the help of these notions and methods the sector structure of the physical state space shall be further clarified, and the interesting connection between (bosonic) superselection charges and geometric symmtries shall be investigated systematically. (H.J. Borchers, D. Buchholz, W. Kunhardt, M. Porrmann, H. Reeh)
Conserved quantities are of great importance for the analysis and, in favourable cases, the complete calculation of the Smatrix in quantum field models. In a programme which has been completed by now, the structure of additive conserved quantities could be clarified fairly completely by rigorous mathematical methods. There are only partial results concerning the interesting cases of charges of higher genus (nonlocal charges). All possible forms of such charges shall be determined within the general framework of quantum field theory. (H. Reeh)
(3) Thermal states
Thermal equilibrium states can be charcterized by the KMS condition valid
for relativistic as well as nonrelativistic systems. J. Bros and D.
Buchholz gave arguments that in relativistic theories a much stronger form
of this condition should hold (relativistic KMS condition). It is to be
checked whether this sharpened version can be derived from a relativistic
condition of passivity of equilibrium states, and what consequences there
are for the structure of relativistic equilibrium states. Generalized KMS
conditions should give rise to new kinds of correlation (in)equalities
which might be useful in statistical mechanics and Euclidean field
theory. (D. Buchholz, M. Requardt, H. Roos)
The concept of a quasiparticle is an important one in statistical mechanics. The development of a general scattering theory for particlelike exitations in thermal states is envisaged on the basis of results by Narnhofer, Requardt and Thirring and recent results of Bros and Buchholz. (D. Buchholz, M. Requardt)
The precise mathematical characterization of thermal nonequilibrium states which are in equilibrium only locally is an important step in the understanding of the structure of thermal processes; furthermore, it is of interest for model calulations. The existing phenomenological ansaetze are partially successful, but they are not at all satisfying given a microscopic point of view. A reformulation of the KMS condition seems necessary and appropriate for this case. With the help of the scaling analysis a generalisation of the notion of temperature ("effective local temperature") is sought for which allows to parametrize local equilibrium states in a consistent way. (M. Requardt, H. Roos)
Dealing with coexisting phases one encounters nontranslation invariant equilibrium states. The study of these states is under way in a long time project. The results are of importance for the understanding of phase boundaries, systems in external fields and in contact with container walls ("wetting"). (M. Requardt)
(4) Gravity and General Relativity:
 (Entanglement) entropy of Black Holes, Holographic bounds (M. Requardt)
 Continuum limit of discrete geometries, understanding of various scales of resolution of spacetime in quantum gravity (M. Requardt)
 Gravitation and Geometry (H. Goenner (retired)):
Alternative and unified theories of gravity (KaluzaKlein, torsion,
scalartensor, Finsler geometry), noncommutative geometry with possible
applications (lattice theory, field theory on discrete spaces, stochastic
processes on manifolds, noncommutative differential calculus,
computer algebra). Foundations of General Relativity and Cosmology.
University of Florida, Gainesville (1),
RIMS Kyoto (3),
CEA Saclay (2,3),
Università di Pisa (2),
Università di Roma (1,2),
Bulgarian Academy of Sciences, Sofia (1,2)
Universität Wien (1)