Search results for "Equations"
showing 10 items of 955 documents
Beyond second-order convergence in simulations of binary neutron stars in full general relativity
2014
Despite the recent rapid progress in numerical relativity, a convergence order less than the second has so far plagued codes solving the Einstein-Euler system of equations. We report simulations of the inspiral of binary neutron stars in quasi-circular orbits computed with a new code employing high-order, high-resolution shock-capturing, finite-differencing schemes that, for the first time, go beyond the second-order barrier. In particular, without any tuning or alignment, we measure a convergence order above three both in the phase and in the amplitude of the gravitational waves. Because the new code is able to calculate waveforms with very small phase errors already at modest resolutions,…
An HLLC Riemann solver for resistive relativistic magnetohydrodynamics
2017
We present a new approximate Riemann solver for the augmented system of equations of resistive relativistic magnetohydrodynamics (RRMHD) that belongs to the family of Harten-Lax-van Leer contact wave (HLLC) solvers. In HLLC solvers, the solution is approximated by two constant states flanked by two shocks separated by a contact wave. The accuracy of the new approximate solver is calibrated through one- and two-dimensional test problems.
Simplifying differential equations for multi-scale Feynman integrals beyond multiple polylogarithms
2017
In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to $\varepsilon$-form.
A model for the very early universe
2008
A model with N species of massless fermions interacting via (microscopic) gravitational torsion in de Sitter spacetime is investigated in the limit N->infinity. The U_V(N)*U_A(N) flavor symmetry is broken dynamically irrespective of the (positive) value of the induced four-fermion coupling. This model is equivalent to a theory with free but massive fermions fluctuating about the chiral condensate. When the fermions are integrated out in a way demonstrated long ago by Candelas and Raine, the associated gap equation together with the Friedmann equation predict that the Hubble parameter vanishes. Introducing a matter sector (subject to a finite gauge symmetry) as a source for subsequent cos…
Simple differential equations for Feynman integrals associated to elliptic curves
2019
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is therefore of current interest, if these methods extend beyond the case of multiple polylogarithms. In this talk I discuss Feynman integrals, which are associated to elliptic curves and their differential equations. I show for non-trivial examples how the system of differential equations can be brought into an $\varepsilon$-form. Single-scale and multi-scale cases are discussed.
Integral Reduction with Kira 2.0 and Finite Field Methods
2021
We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features. The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field methods with the help of FireFly. This procedure can be parallelized on computer clusters with MPI. Furthermore, the support for user-provided systems of equations has been significantly improved. This mode provides the flexibility to integrate Kira into projects that employ specialized reduction formulas, direct reduction of amplitudes, or to problems involving linear system of equations not limited to relations among standard Feynman integrals. We show…
Caustics for spherical waves
2016
We study the development of caustics in shift-symmetric scalar field theories by focusing on simple waves with an $SO(p)$-symmetry in an arbitrary number of space dimensions. We show that the pure Galileon, the DBI-Galileon, and the extreme-relativistic Galileon naturally emerge as the unique set of caustic-free theories, highlighting a link between the caustic-free condition for simple $SO(p)$-waves and the existence of either a global Galilean symmetry or a global (extreme-)relativistic Galilean symmetry.
The 1-loop effective potential for the Standard Model in curved spacetime
2018
The renormalisation group improved Standard Model effective potential in an arbitrary curved spacetime is computed to one loop order in perturbation theory. The loop corrections are computed in the ultraviolet limit, which makes them independent of the choice of the vacuum state and allows the derivation of the complete set of $\beta$-functions. The potential depends on the spacetime curvature through the direct non-minimal Higgs-curvature coupling, curvature contributions to the loop diagrams, and through the curvature dependence of the renormalisation scale. Together, these lead to significant curvature dependence, which needs to be taken into account in cosmological applications, which i…
The Complete Solution of the Classical SL(2,ℝ/U(1) Gauged WZNW Field Theory
1998
We prove that any gauged WZNW model has a Lax pair representation, and give explicitly the general solution of the classical equations of motion of the SL(2,R)/U(1) theory. We calculate the symplectic structure of this solution by solving a differential equation of the Gelfand-Dikii type with initial state conditions at infinity, and transform the canonical physical fields non-locally onto canonical free fields. The results will, finally, be collected in a local B\"acklund transformation. These calculations prepare the theory for an exact canonical quantization.
Amplitudes from superconformal Ward identities
2018
We consider finite superamplitudes of N=1 matter, and use superconformal symmetry to derive powerful first-order differential equations for them. Due to on-shell collinear singularities, the Ward identities have an anomaly, which is obtained from lower-loop information. We show that in the five-particle case, the solution to the equations is uniquely fixed by the expected analytic behavior. We apply the method to a non-planar two-loop five-particle integral.