Further details:
(1) Constructive aspects
A novel approach for the analysis of quantum field theories is based on
an advanced Tomita-Takesaki 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 vacuum-like states in curved space-times 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 half-space. (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
energy-momentum 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 S-matrix 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 (non-local 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 non-relativistic 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
particle-like 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 non-equilibrium 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 non-translation 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 space-time in quantum gravity (M. Requardt)
- Gravitation and Geometry (H. Goenner (retired)):
Alternative and unified theories of gravity (Kaluza-Klein, torsion,
scalar-tensor, Finsler geometry), non-commutative geometry with possible
applications (lattice theory, field theory on discrete spaces, stochastic
processes on manifolds, non-commutative differential calculus,
computer algebra). Foundations of General Relativity and Cosmology.
Members of the Göttingen group are cooperating on the set of problems
mentioned above
with members of the following universities and research institutes:
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)
The group participates in the topic "Foundations of relativistic
quantum physics" within the Graduate Topical Program "Interaction"
of the Evangelisches Studienwerk Villigst, along with Theoretical
Physics Institutes of U Hamburg, FU Berlin, and U Leipzig.
Publications
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
Research reports < 2000
Karl-Henning Rehren