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Transplantation of Local Nets and Geometric Modular Action on Robertson-Walker Space-Times

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arxiv hep-th/0011237 v2 pith:VGZTZ2VB submitted 2000-11-27 hep-th gr-qcmath-phmath.MP

classification hep-thgr-qcmath-phmath.MP
keywords modulargroupsspace-timesactionconditiongeometriclocalnets
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A novel method of transplanting algebras of observables from de Sitter space to a large class of Robertson-Walker space-times is exhibited. It allows one to establish the existence of an abundance of local nets on these spaces which comply with a recently proposed condition of geometric modular action. The corresponding modular symmetry groups appearing in these examples also satisfy a condition of modular stability, which has been suggested as a substitute for the requirement of positivity of the energy in Minkowski space. Moreover, they exemplify the conjecture that the modular symmetry groups are generically larger than the isometry and conformal groups of the underlying space-times.

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  1. Relating the modular Hamiltonian to two-point functions

    math-ph 2025-01 conditional novelty 5.0 of 10

    For free scalar fields in any Gaussian state, the modular Hamiltonian restricted to a region is determined by the equal-time two-point functions X and Π via M=Π^{1/2}B^{-1}arcoth(2B)Π^{1/2}, N=Π^{-1/2}B arcoth(2B)Π^{-...

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