scholarly journals Second order Langevin equation and definition of quantum gravity by stochastic quantisation

2020 ◽  
Vol 957 ◽  
pp. 115090
Author(s):  
Laurent Baulieu ◽  
Siye Wu
Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 171
Author(s):  
Folkert Kuipers ◽  
Xavier Calmet

In this paper, we discuss singularity theorems in quantum gravity using effective field theory methods. To second order in curvature, the effective field theory contains two new degrees of freedom which have important implications for the derivation of these theorems: a massive spin-2 field and a massive spin-0 field. Using an explicit mapping of this theory from the Jordan frame to the Einstein frame, we show that the massive spin-2 field violates the null energy condition, while the massive spin-0 field satisfies the null energy condition, but may violate the strong energy condition. Due to this violation, classical singularity theorems are no longer applicable, indicating that singularities can be avoided, if the leading quantum corrections are taken into account.


2019 ◽  
Vol 19 (02) ◽  
pp. 1950011 ◽  
Author(s):  
Francesco C. De Vecchi ◽  
Paola Morando ◽  
Stefania Ugolini

A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second-order geometry and Itô integration on manifolds, allows us to give a natural and effective definition of Lie symmetries for diffusion processes.


1986 ◽  
Vol 59 (2) ◽  
pp. 683-693 ◽  
Author(s):  
Samuel E. Krug ◽  
Edgar F. Johns

The second-order factors structure of the 16 Personality Factor Questionnaire (16PF) was cross-validated on a large sample ( N = 17,381) of normal males and females. Subjects were sampled across a broad range of ages, socioeconomic levels, education, geographic location, and ethnicity. The purposes of this investigation were (1) to provide a precise definition of 16PF second-order factor structure, (2) to shed additional light on the nature of two second-order factors that have been previously identified but described as “unstable” and “poorly reproduced,” and (3) to determine the extent to which common factor estimation formulas for men and women would prove satisfactory for applied work. The resulting solutions were congruent with previous studies and showed a high degree of simple structure. Support was provided for one, but not both, of the two additional second-order factors. Results also supported the use of simplified estimation formulas for applied use.


2021 ◽  
pp. 121-165
Author(s):  
Adrian Tanasa

This chapter is the first chapter of the book dedicated to the study of the combinatorics of various quantum gravity approaches. After a brief introductory section to quantum gravity, we shortly mention the main candidates for a quantum theory of gravity: string theory, loop quantum gravity, and group field theory (GFT), causal dynamical triangulations, matrix models. The next sections introduce some GFT models such as the Boulatov model, the colourable and the multi-orientable model. The saddle point method for some specific GFT Feynman integrals is presented in the fifth section. Finally, some algebraic combinatorics results are presented: definition of an appropriate Conne–Kreimer Hopf algebra describing the combinatorics of the renormalization of a certain tensor GFT model (the so-called Ben Geloun–Rivasseau model) and the use of its Hochschild cohomology for the study of the combinatorial Dyson–Schwinger equation of this specific model.


1990 ◽  
Vol 247 (4) ◽  
pp. 537-542 ◽  
Author(s):  
Enzo Marinari ◽  
Giorgio Parisi

2003 ◽  
Vol 35 (02) ◽  
pp. 395-416 ◽  
Author(s):  
A. Gefferth ◽  
D. Veitch ◽  
I. Maricza ◽  
S. Molnár ◽  
I. Ruzsa

A new treatment of second-order self-similarity and asymptotic self-similarity for stationary discrete time series is given, based on the fixed points of a renormalisation operator with normalisation factors which are not assumed to be power laws. A complete classification of fixed points is provided, consisting of the fractional noise and one other class. A convenient variance time function approach to process characterisation is used to exhibit large explicit families of processes asymptotic to particular fixed points. A natural, general definition of discrete long-range dependence is provided and contrasted with common alternatives. The closely related discrete form of regular variation is defined, its main properties given, and its connection to discrete self-similarity explained. Folkloric results on long-range dependence are proved or disproved rigorously.


2007 ◽  
Vol 64 (2) ◽  
pp. 665-669 ◽  
Author(s):  
E. Bouzereau ◽  
L. Musson-Genon ◽  
B. Carissimo

Abstract In subgrid-scale condensation schemes of cloud models, the majority of previous authors have relied on results presented in a paper by Bougeault. In the present paper, second-order liquid water correlations are restated that differ from the former paper but are coherent with the corrigendum of Mellor. These differences are explained here through two different underlying definitions of cloud water content fluctuations; they can be summarized by whether or not unsaturated air within a grid box contributes to the eddy flux of the cloud water content. Taking into account the issue mentioned above, the “buoyancy flux” is also derived. Although the full impact of these changes has not been evaluated here, it may become important for future global cloud-resolving climate models.


2018 ◽  
Vol 15 (08) ◽  
pp. 1830003 ◽  
Author(s):  
Víctor Manuel Jiménez ◽  
Manuel de León ◽  
Marcelo Epstein

A Lie groupoid, called second-order non-holonomic material Lie groupoid, is associated in a natural way to any Cosserat medium. This groupoid is used to give a new definition of homogeneity which does not depend on a material archetype. The corresponding Lie algebroid, called second-order non-holonomic material Lie algebroid, is used to characterize the homogeneity property of the material. We also relate these results with the previously obtained ones in terms of non-holonomic second-order [Formula: see text]-structures.


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