Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields

Abstract

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.

27 pages, v3: result improved by eliminating redundant assumption

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Cited by in corpus (13)

• Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory
• Constraining conformal field theory with higher spin symmetry in four dimensions
• Jorge A. Swieca's contributions to quantum field theory in the 60s and 70s and their relevance in present research
• Harmonic bilocal fields generated by globally conformal invariant scalar fields
• Jacobi Identity for Vertex Algebras in Higher Dimensions
• Semibounded representations of hermitian Lie groups
• Conformal field theories with infinitely many conservation laws
• Infinite dimensional Lie algebras in 4D conformal quantum field theory
• Pole structure and biharmonic fields in conformal QFT in four dimensions
• New methods in conformal partial wave analysis
• Minimal representations and reductive dual pairs in conformal field theory
• Semibounded representations and invariant cones in infinite dimensional Lie algebras
• Massless Wigner particles in conformal field theory are free