Search results for "Mathematical physics"
showing 10 items of 2687 documents
Comparison between the fCCZ4 and BSSN formulations of Einstein equations in spherical polar coordinates
2015
Recently, we generalized a covariant and conformal version of the Z4 system of the Einstein equations using a reference metric approach, that we denote as fCCZ4. We successfully implemented and tested this approach in a 1D code that uses spherical coordinates and assumes spherical symmetry, obtaining from one to three orders of magnitude reduction of the Hamiltonian constraint violations with respect to the BSSN formulation in tests involving neutron star spacetimes. In this work, we show preliminary results obtained with the 3D implementation of the fCCZ4 formulation in a fully 3D code using spherical polar coordinates.
On the local existence of maximal slicings in spherically symmetric spacetimes
2010
In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution may be accomplished analytical or numerically. We provide a general procedure to construct such maximal slicings.
Appell Functions and the Scalar One-Loop Three-point Integrals in Feynman Diagrams
2002
The scalar three-point function appearing in one-loop Feynman diagrams is compactly expressed in terms of a generalized hypergeometric function of two variables. Use is made of the connection between such Appell function and dilogarithms coming from a previous investigation. Special cases are obtained for particular values of internal masses and external momenta.
Group-Theoretic analysis of the mixing angle in the electroweak gauge group
1996
In this paper the authors provide strong mathematical support for the idea that the experimentally measured magnitude 1 - M{sub W}{sup 2}/M{sub Z}{sup 2} associated with sin{sup 2}{theta}{sub w} in the standard model of electroweak interactions cannot be simultaneously identified with the squared quotient of the electric charge by the SU(2) charge, e{sup 2}/g{sup 2}. In fact, the natural, mathematical requirement that the Weinberg rotation between the gauge fields associated with the third component of the {open_quotes}weak isospin{close_quotes} (T{sub 3}) and the hypercharge (Y) proceeds from a global Lie-group homomorphism of the SU(2) {circle_times} U(1){sub y} gauge group in some locall…
Labeling spherically symmetric spacetimes with the Ricci tensor
2017
We complete the intrinsic characterization of spherically symmetric solutions partially accomplished in a previous paper [Class.Quant.Grav. (2010) 27 205024]. In this approach we consider every compatible algebraic type of the Ricci tensor, and we analyze specifically the conformally flat case for perfect fluid and Einstein-Maxwell solutions. As a direct application we obtain the {\em ideal} labeling (exclusively involving explicit concomitants of the metric tensor) of the Schwarzschild interior metric and the Vaidya solution. The Stephani universes and some significative subfamilies are also characterized.
Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity
2001
Homogeneous and isotropic cosmologies of the Planck era before the classical Einstein equations become valid are studied taking quantum gravitational effects into account. The cosmological evolution equations are renormalization group improved by including the scale dependence of Newton's constant and of the cosmological constant as it is given by the flow equation of the effective average action for gravity. It is argued that the Planck regime can be treated reliably in this framework because gravity is found to become asymptotically free at short distances. The epoch immediately after the initial singularity of the Universe is described by an attractor solution of the improved equations w…
Inflation, renormalization, and CMB anisotropies
2010
5 páginas.-- Trabajo presentado al Spanish Relativity Meeting (ERE 2009).-- El PDF es la versión pre-print (arXiv:1002.3914v1).
Spiral Inflation with Coleman-Weinberg Potential
2015
We apply the idea of spiral inflation to Coleman-Weinberg potential, and show that inflation matching well observations is allowed for a symmetry-breaking scale ranging from an intermediate scale to GUT scale even if the quartic coupling $\lambda$ is of $\mathcal{O}(0.1)$. The tensor-to-scalar ratio can be of $\mathcal{O}(0.01)$ in case of GUT scale symmetry-breaking.
Instantons and theΔI=1/2Rule
2001
The instanton-induced interaction leads to a significant enhancement of the Ao weak amplitude determining the DeltaI = 1/2 rule, through the contribution of operators with dimension d = 9, as we show in the weak K--> pi(pi) decay.
Relaxation of periodic and nonstandard growth integrals by means of two-scale convergence
2019
An integral representation result is obtained for the variational limit of the family functionals $\int_{\Omega}f\left(\frac{x}{\varepsilon}, Du\right)dx$, as $\varepsilon \to 0$, when the integrand $f = f (x,v)$ is a Carath\'eodory function, periodic in $x$, convex in $v$ and with nonstandard growth.