Mathematical Physics Group

  KTH Theoretical Physics, AlbaNova

  SE-106 91 Stockholm SWEDEN

Research interests

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 promising a deeper understanding of central issues such as regularization and renormalization. We have been interested in gauge theories and associated anomalies where the noncommutative nature of quantum systems and the geometric nature of 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

(Edwin Langmann)

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

(Edwin Langmann)

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.

KEYWORDS: Quantum Chaos, Correlation functions, Dissipation, Entropy, Ergodicity, Information

UP    Edwin Langmann  Last modified May 5, 2008