Search results for "Mathematical physics"
showing 10 items of 2687 documents
Junction conditions in Palatinif(R) gravity
2020
We work out the junction conditions for $f(R)$ gravity formulated in metric-affine (Palatini) spaces using a tensor distributional approach. These conditions are needed for building consistent models of gravitating bodies with an interior and exterior regions matched at some hypersurface. Some of these conditions depart from the standard Darmois-Israel ones of General Relativity and from their metric $f(R)$ counterparts. In particular, we find that the trace of the stress-energy momentum tensor in the bulk must be continuous across the matching hypersurface, though its normal derivative need not to. We illustrate the relevance of these conditions by considering the properties of stellar sur…
On weak solutions of linear coercive integral equations in spacesL 2(X; ℋ k )
1989
Пусть (X,A, μ) - полное про странство с σ-конечно й мерой, и пусть\(\overline {\mu \times \mu } \). - замык ание меры μ×μ. Пусть далееg: X×X→C - квадратично интегрируемая функц ия по мере\(\overline {\mu \times \mu } \). Рассматривается лин ейное интегральное у равнение (слабого) типа (1) $$u(t) + A(\mathop \smallint \limits_x g(t,s)u(s)d\mu ) = f(t)\Pi .B.B\,X,$$ (1) гдеА - максимальное р асширение L k ′ (в простр анстве ХeрмандераH 1=B2к) соотв ествующего линейного (псевдодиф ференциального) опер атораL: S→S; иS обозначает класс Щварца функций Rn→-C. Уст анавливается сущест вование (слабых) решений (1) при н екотором условии коэрпитивно сти на оператор (2) $$(L\Psi )(t) = \Psi (t) + \int\…
Umbilicity of space-like submanifolds of Minkowski space
2004
We study some properties of space-like submanifolds in Minkowski n-space, whose points are all umbilic with respect to some normal field. As a consequence of these and some results contained in a paper by Asperti and Dajczer, we obtain that being ν-umbilic with respect to a parallel light-like normal field implies conformal flatness for submanifolds of dimension n − 2 ≥ 3. In the case of surfaces, we relate the umbilicity condition to that of total semi-umbilicity (degeneracy of the curvature ellipse at every point). Moreover, if the considered normal field is parallel, we show that it is everywhere time-like, space-like or light-like if and only if the surface is included in a hyperbolic 3…
Birkhoff's theorem and perturbations in $f(R)$ theories
2012
Invited contribution to Annalen der Physik (Expert Opinion).
On the convergence of perturbative coupled cluster triples expansions:Error cancellations in the CCSD(T) model and the importance of amplitude relaxa…
2015
Recently, we proposed a novel Lagrangian-based perturbation series-the CCSD(T-n) series-which systematically corrects the coupled cluster singles and doubles (CCSD) energy in orders of the Møller-Plesset fluctuation potential for effects due to triple excitations. In the present study, we report numerical results for the CCSD(T-n) series up through fourth order which show the predicted convergence trend throughout the series towards the energy of its target, the coupled cluster singles, doubles, and triples (CCSDT) model. Since effects due to the relaxation of the CCSD singles and doubles amplitudes enter the CCSD(T-n) series at fourth order (the CCSD(T-4) model), we are able to separate th…
Ebene Wellen endlicher Amplitude in idealen Gasen
1951
Der physikalische Zustand in einer ebenen Welle endlicher Amplitude läßt sich durch die Größen ν = αc + u und ω = Δc - u beschreiben; c ist die Schallgeschwindigkeit, u die Strömungsgeschwindigkeit, α die Zahl der Freiheitsgrade der Gasmoleküle (§ 2). Häufig ist es bequemer, statt v, ω die Schallgeschwindigkeiten cv, cw oder die Drucke pv, pw zu verwenden, welche zu den beiden fortschreitenden Wellen gehören würden, die aus der v- und ω-Welle entstünden, wenn die v- und ω-Wellen sich einzeln in ungestörtem Gebiet ausbreiten könnten (§ 3). Mit diesen Größen lassen sich Vorgänge der Reflexion und der Rohrströmung besonders einfach beschreiben. Behandelt werden: Reflexion an einer festen Wand,…
Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD.
2019
We present the three-pion spectrum with maximal isospin in a finite volume determined from lattice QCD, including excited states in addition to the ground states across various irreducible representations at zero and nonzero total momentum. The required correlation functions, from which the spectrum is extracted, are computed using a newly implemented algorithm which speeds up the computation by more than an order of magnitude. On a subset of the data we extract a nonzero value of the three-pion threshold scattering amplitude using the $1/L$ expansion of the three-particle quantization condition, which consistently describes all states at zero total momentum. The finite-volume spectrum is p…
Is There a C-Function in 4D Quantum Einstein Gravity?
2016
We describe a functional renormalization group-based method to search for ‘C-like’ functions with properties similar to that in 2D conformal field theory. It exploits the mode counting properties of the effective average action and is particularly suited for theories including quantized gravity. The viability of the approach is demonstrated explicitly in a truncation of 4 dimensional Quantum Einstein Gravity, i.e. asymptotically safe metric gravity.
Interpreting deviations between AR-VTG and GR
2019
The cosmic microwave background (CMB) anisotropies predicted by two cosmological models are compared, one of them is the standard model of general relativity with cold dark matter and cosmological constant, whereas the second model is based on a consistent vector-tensor theory of gravitation explaining solar system and cosmological observations. It is proved that the resulting differences — between the anisotropies of both models — are due to the so-called late integrated Sachs–Wolfe effect and, consequently, cross-correlations between maps of CMB temperatures and tracers of the dark matter distribution could be used in future to select one of the above models. The role of reionization is …
Simplicial Wheeler-DeWitt equation in 2+1 spacetime dimensions.
1993
We introduce an equation which rue suggest to be a simplicial counterpart to the Wheeler-DeWitt equation in 2 + 1 spacetime dimensions. Our approach is based on the use of the Ashtekar variables