GEOMETRIC MODULAR ACTION AND SPACETIME SYMMETRY GROUPS

DOI10.1142/S0129055X00000174zbMATH Open1044.81082arXivmath-ph/9805026OpenAlexW1988271726MaRDI QIDQ4519847

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Publication date: 4 December 2000

Published in: (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/math-ph/9805026

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