MODULAR LOCALIZATION AND WIGNER PARTICLES
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Publication:4420455
DOI10.1142/S0129055X02001387zbMATH Open1033.81063arXivmath-ph/0203021OpenAlexW2077034480MaRDI QIDQ4420455
Author name not available (Why is that?)
Publication date: 17 August 2003
Published in: (Search for Journal in Brave)
Abstract: We propose a framework for the free field construction of algebras of local observables which uses as an input the Bisognano-Wichmann relations and a representation of the Poincare' group on the one-particle Hilbert space. The abstract real Hilbert subspace version of the Tomita-Takesaki theory enables us to bypass some limitations of the Wigner formalism by introducing an intrinsic spacetime localization. Our approach works also for continuous spin representations to which we associate a net of von Neumann algebras on spacelike cones with the Reeh-Schlieder property. The positivity of the energy in the representation turns out to be equivalent to the isotony of the net, in the spirit of Borchers theorem. Our procedure extends to other spacetimes homogeneous under a group of geometric transformations as in the case of conformal symmetries and de Sitter spacetime.
Full work available at URL: https://arxiv.org/abs/math-ph/0203021
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