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Geometric Modular Action and Spacetime Symmetry Groups

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arxiv math-ph/9805026 v2 pith:C7BV2ITG submitted 1998-05-28 math-ph gr-qchep-thmath.MP

classification math-phgr-qchep-thmath.MP
keywords conditiongroupsmodularspace-timesstatesactiongeometricproposed
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A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides these groups with projective representations. Under suitable additional conditions, these groups induce groups of point transformations on these space-times, which may be interpreted as symmetry groups. The consequences of this condition are studied in detail in application to two concrete space-times -- four-dimensional Minkowski and three-dimensional de Sitter spaces -- for which it is shown how this condition characterizes the states invariant under the respective isometry group. An intriguing new algebraic characterization of vacuum states is given. In addition, the logical relations between the condition proposed in this paper and the condition of modular covariance, widely used in the literature, are completely illuminated.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 95 citations worldwide. Full citation record

  1. Petz-R\'enyi relative entropy in QFT from modular theory

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    Petz-Renyi relative entropy for coherent excitations of free quantum fields is computed from modular theory and shown to involve the symmetric part of the two-point function, unlike relative entropy.

  2. Numerical approach to the modular operator for fermionic systems

    math-ph 2026-05 unverdicted novelty 6.0 of 10

    A position-space discretization on a cylinder approximates the modular operator for one and two double cones in the 1+1D massive Majorana field, showing nontrivial mass dependence and reduced bilocal terms at higher masses.

  3. Spacetime from Operator Algebras

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    Reconstructs spacetime metric, curvature, and Einstein equations from matter field operator algebras in the G to 0 limit without using Bekenstein-Hawking area law, then models finite-N discrete spectra via random matr...

  4. 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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