Mathematical Physics Group
KTH Theoretical Physics, AlbaNova
SE-106 91 Stockholm SWEDEN
Mathematical aspects of quantum field theory
(Jouko Mickelsson, Edwin Langmann)
Despite of our extensive knowledge on quantum field theory (QFT) we are
still lacking a complete conceptual and mathematical understanding of
it. Noncommutative geometry (NCG) is a powerful mathematical framework
a deeper understanding of central issues such as regularization and
We have been interested in gauge theories and associated anomalies
the noncommutative nature of quantum systems and the geometric nature
gauge fields can be united into a coherent picture. Our aim is not only
a better understanding of QFT but also to obtain novel results in
mathematics, in particular noncommutative geometry, which are
interesting in their own right.
KEYWORDS: Renormalization, noncommutative geometry, K-theory,
current algebras, anomalies, gerbes
Exactly solvable systems
We are studying exactly solvable classical and quantum
many-body systems, for example models with local interactions which can
be solved using Bethe ansatz, or Calogero-Sutherland like systems. We
are also interested in the relation of such systems to gauge theories,
conformal field theory, and special functions.
KEYWORDS: Calogero-Sutherland models, special functions, gauge
theories, conformal field theory.
Strongly interacting boson and fermion systems
We are interested in strongly interacting systems of fermions in two
dimensions which are relevant for high temperature superconductors or
the fractional quantum Hall effect. Our aim is to develop more reliable
computational tools and a better mathematical understanding of such
systems. We try to find and study
exactly solvable models relevant in this context. We also study
strongly interacting boson models relevant for Bose-Einstein
condensation of Alkali atoms, e.g.
KEYWORDS: Hubbard model, Luttinger model, bosonization,
exactly solvable systems, high temperature superconductors, fractional
quantum Hall effect, Bose-Einstein condensation
Quantum Dynamical Systems
(Göran Lindblad, Edwin Langmann)
Models of quantum dynamics capable of describing relaxation
and fluctuations are studied using several different mathematical
methods, e.g. quantum information theory and operator algebra methods.
Results include no-go theorems on the the existence of reduced dynamics
of open quantum systems as an exact description of the quantum
correlation functions. There is also a characterization of determinism
versus randomness of the correlation functions using spectral
properties or entropy measures of information.
Subjects for further study are: the transition from
deterministic to chaotic behavior, quantum localization and transient
quantum chaos, low temperature dissipation, the quantum-classical
transition through decoherence. Possible applications include quantum
information transmission and quantum computation.
Quantum Chaos, Correlation functions, Dissipation, Entropy, Ergodicity,
Last modified May 5, 2008