Search results for " Transformation"
showing 10 items of 1043 documents
Ghosts in metric-affine higher order curvature gravity
2019
We disprove the widespread belief that higher order curvature theories of gravity in the metric-affine formalism are generally ghost-free. This is clarified by considering a sub-class of theories constructed only with the Ricci tensor and showing that the non-projectively invariant sector propagates ghost-like degrees of freedom. We also explain how these pathologies can be avoided either by imposing a projective symmetry or additional constraints in the gravity sector. Our results put forward that higher order curvature gravity theories generally remain pathological in the metric-affine (and hybrid) formalisms and highlight the key importance of the projective symmetry and/or additional co…
Scattering amplitudes in affine gravity
2020
Affine gravity is a connection-based formulation of gravity that does not involve a metric. After a review of basic properties of affine gravity, we compute the tree-level scattering amplitude of scalar particles interacting gravitationally via the connection in a curved spacetime. We find that, while classically equivalent to general relativity, affine gravity differs from metric quantum gravity.
Enumerating higher-dimensional operators with on-shell amplitudes
2020
We establish a simple formula for the minimal dimension of operators leading to any helicity amplitude. It eases the systematic enumeration of independent operators from the construction of massless non-factorizable on-shell amplitudes. Little-group constraints can then be solved algorithmically for each helicity configuration to extract a complete set of spinor structures with lowest dimension. Occasionally, further reduction using momentum conservation, on-shell conditions and Schouten identities is required. A systematic procedure to account for the latter is presented. Dressing spinor structures with dot products of momenta finally yields the independent Lorentz structures for each heli…
Superfield commutators for D = 4 chiral multiplets and their apppications
1987
The superfield commutators and their corresponding equal-time limits are derived in a covariant way for the D=4 free massive chiral multiplet. For interesting chiral multiplets, the general KAllen-Lehmann representation is also introduced. As applications of the free superfield commutators, the general solution of the Cauchy problem for chiral superfields is given, and an analysis of the closure of the bilinear products of superfields which desrcibe the extension of the internal currents for free supersymmetric chiral matter is performed.
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.
Arbitrary qudit gates by adiabatic passage
2013
We derive an adiabatic technique that implements the most general SU($d$) transformation in a quantum system of $d$ degenerate states, featuring a qudit. This technique is based on the factorization of the SU($d$) transformation into $d$ generalized quantum Householder reflections, each of which is implemented by a two-shot stimulated Raman adiabatic passage with appropriate static phases. The energy of the lasers needed to synthesize a single Householder reflection is shown to be remarkably constant as a function of $d$. This technique is directly applicable to a linear trapped ion system with $d+1$ ions. We implement the quantum Fourier transform numerically in a qudit with $d=4$ (defined…
Nonlinear stability of relativistic sheared planar jets
2005
The linear and non-linear stability of sheared, relativistic planar jets is studied by means of linear stability analysis and numerical hydrodynamical simulations. Our results extend the previous Kelvin-Hemlholtz stability studies for relativistic, planar jets in the vortex sheet approximation performed by Perucho et al. (2004a,b) by including a shear layer between the jet and the external medium and more general perturbations. The models considered span a wide range of Lorentz factors ($2.5-20$) and internal energies ($0.08 c^2-60 c^2$) and are classified into three classes according to the main characteristics of their long-term, non-linear evolution. We observe a clear separation of thes…
Resonant Kelvin-Helmholtz modes in sheared relativistic flows
2007
Qualitatively new aspects of the (linear and non-linear) stability of sheared relativistic (slab) jets are analyzed. The linear problem has been solved for a wide range of jet models well inside the ultrarelativistic domain (flow Lorentz factors up to 20; specific internal energies $\approx 60c^2$). As a distinct feature of our work, we have combined the analytical linear approach with high-resolution relativistic hydrodynamical simulations, which has allowed us i) to identify, in the linear regime, resonant modes specific to the relativistic shear layer ii) to confirm the result of the linear analysis with numerical simulations and, iii) more interestingly, to follow the instability develo…
Which physical parameters can be inferred from the emission variability of relativistic jets?
2005
We present results of a detailed numerical study and theoretical analysis of the dynamics of internal shocks in relativistic jets and the non-thermal flares associated with these shocks. In our model internal shocks result from collisions of density inhomogeneities (shells) in relativistic jet flows. We find that the merged shell resulting from the inelastic collision of shells has a complicated internal structure due to the non-linear dynamics of the interaction. Furthermore, the instantaneous efficiency for converting kinetic energy into thermal energy is found to be almost twice as high as theoretically expected during the period of significant emission. The Lorentz factors of the intern…
An alternative formulation of Classical Mechanics based on an analogy with Thermodynamics
2013
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of transformations are considered, the new formulation is found to be completly equivalent to the usual Lagrangian formulation, recovering well established results like the conservation of the angular momentum. Furthermore, a natural generalization of the Poisson Bracket is found to be inherent to the formalism introduced. On the other hand, we find that with a convenient redefinition of the Lagrangian, $\mathcal{L}^{\prime}=-\mathcal{L}$, it is possible to establish an …