The random discrete action for two-dimensional spacetime

• Verfasst von: Benincasa, Dionigi M. T. [VerfasserIn]
• Verfasst von: Dowker, Fay [VerfasserIn]
• Verfasst von: Schmitzer, Bernhard [VerfasserIn]
• Titel: The random discrete action for two-dimensional spacetime
• Verf.angabe: Dionigi MT Benincasa, Fay Dowker and Bernhard Schmitzer
• E-Jahr: 2011
• Jahr: 20 April 2011
• Umfang: 16 S.
• Fussnoten: Gesehen am 16.03.2022
• Titel Quelle: Enthalten in: Classical and quantum gravity
• Ort Quelle: Bristol : IOP Publ., 1984
• Jahr Quelle: 2011
• Band/Heft Quelle: 28(2011), 10, Artikel-ID 105018, Seite 1-16
• ISSN Quelle: 1361-6382
• DOI: doi:10.1088/0264-9381/28/10/105018
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1795792507

Abstract

A one-parameter family of random variables, called the Discrete Action, is defined for a two-dimensional Lorentzian spacetime of finite volume. The single parameter is a discreteness scale. The expectation value of this discrete action is calculated for various regions of 2D Minkowski spacetime, . When a causally convex region of is divided into subregions using null lines the mean of the discrete action is equal to the alternating sum of the numbers of vertices, edges and faces of the null tiling, up to corrections that tend to 0 as the discreteness scale is taken to 0. This result is used to predict that the mean of the discrete action of the flat Lorentzian cylinder is zero up to corrections, which is verified. The ‘topological’ character of the discrete action breaks down for causally convex regions of the flat trousers spacetime that contain the singularity and for non-causally convex rectangles.