Geometric modular action and spacetime symmetry groups

Citation
D. Buchholz et al., Geometric modular action and spacetime symmetry groups, REV MATH PH, 12(4), 2000, pp. 475-560
Citations number
87
Language
INGLESE
art.tipo
Review
Categorie Soggetti
Physics
Journal title
REVIEWS IN MATHEMATICAL PHYSICS
ISSN journal
0129-055X → ACNP
Volume
12
Issue
4
Year of publication
2000
Pages
475 - 560
Database
ISI
SICI code
0129-055X(200004)12:4<475:GMAASS>2.0.ZU;2-Q
Abstract
A condition of geometric modular action is proposed as a selection principl e for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered set s 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 con sequences of this condition are studied in detail in application to two con crete spacetimes - four-dimensional Minkowski and three-dimensional de Sitt er spaces - for which it is shown how this condition characterizes the stat es invariant under the respective isometry group. An intriguing new algebra ic characterization of vacuum states is given. In addition, the logical rel ations between the condition proposed in this paper and the condition of mo dular covariance, widely used in the literature, are completely illuminated .