scholarly journals Gauge-invariant description of weak gravitational field on a spherically symmetric background with cosmological constant

2019 ◽  
Vol 36 (21) ◽  
pp. 215006
Author(s):  
Piotr Waluk ◽  
Jacek Jezierski
Keyword(s):  
Gravitational Field ◽  
Cosmological Constant ◽  
Spherically Symmetric ◽  
Gauge Invariant ◽  
Weak Gravitational Field ◽  
Invariant Description

Casimir effects are not an experimental demonstration that free vacuum gravitates: connections to the Cosmological Constant Problem

2015 ◽  
Vol 24 (12) ◽  
pp. 1544020 ◽  
Author(s):  
Massimo Cerdonio ◽  
Carlo Rovelli
Keyword(s):  
Gravitational Field ◽  
Cosmological Constant ◽  
Casimir Force ◽  
Mechanical Equilibrium ◽  
Experimental Demonstration ◽  
Cosmological Constant Problem ◽  
Plane Parallel ◽  
Weak Gravitational Field ◽  
Basic Physics ◽  
Concrete Model

We discuss a concrete model of a Casimir cavity, with plane parallel metallic plates kept in mechanical equilibrium by a spring and placed in a weak gravitational field. We show that simple basic physics implies that the plates cannot be idealized as massless and therefore the effect of the vacuum is inextricably connected with the interaction with the matter of the plates. In Casimir cavities, it is a vacuum bound by matter which is at work. Therefore, the existence of the Casimir force does not imply that free vacuum gravitates and contributes to the cosmological constant.

scholarly journals Notes on cluster algebras and some all-loop Feynman integrals

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Qinglin Yang
Keyword(s):  
Configuration Space ◽  
Strong Evidence ◽  
Wilson Loop ◽  
Cluster Algebra ◽  
Cluster Algebras ◽  
Gauge Invariant ◽  
Feynman Integrals ◽  
Cluster Function ◽  
Invariant Description ◽  
Cluster Configuration

Abstract We study cluster algebras for some all-loop Feynman integrals, including box-ladder, penta-box-ladder, and double-penta-ladder integrals. In addition to the well-known box ladder whose symbol alphabet is $$ {D}_2\simeq {A}_1^2 $$ D 2 ≃ A 1 2 , we show that penta-box ladder has an alphabet of D3 ≃ A3 and provide strong evidence that the alphabet of seven-point double-penta ladders can be identified with a D4 cluster algebra. We relate the symbol letters to the u variables of cluster configuration space, which provide a gauge-invariant description of the cluster algebra, and we find various sub-algebras associated with limits of the integrals. We comment on constraints similar to extended-Steinmann relations or cluster adjacency conditions on cluster function spaces. Our study of the symbol and alphabet is based on the recently proposed Wilson-loop d log representation, which allows us to predict higher-loop alphabet recursively; by applying it to certain eight-point and nine-point double-penta ladders, we also find D5 and D6 cluster functions respectively.

scholarly journals Some effects on relativistic quantum systems due to a weak gravitational field

2005 ◽  
Vol 35 (4b) ◽  
pp. 1110-1112 ◽  
Author(s):  
Geusa de A. Marques ◽  
Sandro G. Fernandes ◽  
V. B. Bezerra
Keyword(s):  
Gravitational Field ◽  
Relativistic Quantum ◽  
Quantum Systems ◽  
Weak Gravitational Field
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