Communications in Mathematical Physics

, Volume 271, Issue 1, pp 223–246 | Cite as

Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields

  • Bojko Bakalov
  • Nikolay M. Nikolov
  • Karl-Henning RehrenEmail author
  • Ivan Todorov


The superselection sectors of two classes of scalar bilocal quantum fields in D ≥ 4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective gauge groups U(N) and O(N) confirms the expectations based on general results obtained in the framework of local nets in algebraic quantum field theory, but the approach using standard Lie algebra methods rather than abstract duality theory is complementary. The result indicates that one does not lose interesting models if one postulates the absence of scalar fields of dimension D−2 in models with global conformal invariance. Another remarkable outcome is the observation that, with an appropriate choice of the Hamiltonian, a Lie algebra embedded into the associative algebra of observables completely fixes the representation theory.


Gauge Group Commutation Relation Young Diagram Irreducible Unitary Representation Vertex Algebra 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Bojko Bakalov
    • 1
  • Nikolay M. Nikolov
    • 2
    • 3
  • Karl-Henning Rehren
    • 3
    Email author
  • Ivan Todorov
    • 2
    • 3
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.Institute for Nuclear Research and Nuclear EnergySofiaBulgaria
  3. 3.Institut für Theoretische PhysikUniversität GöttingenGöttingenGermany

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