Partial wave expansion and Wightman positivity in conformal field theory

2005/04/29 by Nikolay Nikolov, N. M. Nikolov, K. -H. Rehren +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Chromodynamics and Particle Interactions #hep-th #math-ph #math.MP

paper · pdf · doi:10.1016/j.nuclphysb.2005.06.006

published as Nucl.Phys. B722 (2005) 266-296 · 26 pages. v2: references and comments added, numerical errors corrected

arxiv created 2005/04/29 · openalex publication_date 2005/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

A new method for computing exact conformal partial wave expansions is developed and applied to approach the problem of Hilbert space (Wightman) positivity in a non-perturbative four-dimensional quantum field theory model. The model is based on the assumption of global conformal invariance on compactified Minkowski space. Bilocal fields arising in the harmonic decomposition of the operator product expansion prove to be a powerful instrument in exploring the field content. In particular, in the theory of a field of dimension 4 which has the properties of a (gauge invariant) Lagrangian, the scalar field contribution to the 6-point function of the twist 2 bilocal field is analyzed with the aim to separate the free field part from the nontrivial part.

Citations

• Vertex Algebras in Higher Dimensions and Globally Conformal Invariant Quantum Field Theory
• Rationality of Conformally Invariant Local Correlation Functions on Compactified Minkowski Space

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