caa a22 4500 445387734 CHVBK 20180317143037.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s10714-011-1227-1 doi (NATIONALLICENCE)springer-10.1007/s10714-011-1227-1 Khatsymovsky V. Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia aut Gravity action on rapidly varying metrics [Elektronische Daten] [V. Khatsymovsky] We consider a four-dimensional simplicial complex and the minisuperspace general relativity system on it. The metric is flat in most parts of the interior of every 4-simplex, with the exception of a thin layer of thickness $${\propto \varepsilon}$$ along each three-dimensional face. In this layer the metric undergoes a jump between the two 4-simplices sharing this face. At $${\varepsilon \to 0}$$ this jump would become a discontinuity. However, a discontinuity of the metric induced on the face is not allowed in general relativity: terms arise in the Einstein action tending to infinity as $${\varepsilon \to 0}$$ . In the path integral approach, these terms lead to the pre-exponent factor with δ-functions requiring that the metric induced on the faces be continuous. That is, the 4-simplices fit on their common faces. The other part of the path integral measure corresponds to the action, which is the sum of independent terms over the 4-simplices. Therefore this part of the path integral measure is the product of independent measures over the 4-simplices. The result obtained is in accordance with our previous one obtained from symmetry considerations. Springer Science+Business Media, LLC, 2011 Path integral nationallicence Piecewise flat spacetime nationallicence Generalized function nationallicence General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/11(2011-11-01), 3127-3138 0001-7701 43:11<3127 2011 43 10714 https://doi.org/10.1007/s10714-011-1227-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-011-1227-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Khatsymovsky V. Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia aut NATIONALLICENCE 773 0- General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/11(2011-11-01), 3127-3138 0001-7701 43:11<3127 2011 43 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer