Search results for "TRANSFORMATION"
showing 10 items of 1634 documents
Anisotropic deformations in a class of projectively-invariant metric-affine theories of gravity
2020
Among the general class of metric-affine theories of gravity, there is a special class conformed by those endowed with a projective symmetry. Perhaps the simplest manner to realise this symmetry is by constructing the action in terms of the symmetric part of the Ricci tensor. In these theories, the connection can be solved algebraically in terms of a metric that relates to the spacetime metric by means of the so-called deformation matrix that is given in terms of the matter fields. In most phenomenological applications, this deformation matrix is assumed to inherit the symmetries of the matter sector so that in the presence of an isotropic energy-momentum tensor, it respects isotropy. In th…
On the Weyl transverse frames in type I spacetimes
2004
We apply a covariant and generic procedure to obtain explicit expressions of the transverse frames that a type I spacetime admits in terms of an arbitrary initial frame. We also present a simple and general algorithm to obtain the Weyl scalars $\Psi_2^T$, $\Psi_0^T$ and $\Psi_4^T$ associated with these transverse frames. In both cases it is only necessary to choose a particular root of a cubic expression.
Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
1996
We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms. Second, we define gauge invariance to an arbitrary order $n$. Finally, we give a generating formula for the gauge transformation to an arbitrary order and explicit rules to second and third order. This formalism can be used in any field of applied general relativity, such as cosmological and black hole perturbations, as well …
Effects of the Lorentz invariance violation in Coulomb interaction in nuclei and atoms
2016
Anisotropy in the speed of light that has been constrained by Michelson-Morley-type experiments also generates anisotropy in the Coulomb interactions. This anisotropy can manifest itself as an energy anisotropy in nuclear and atomic experiments. Here the experimental limits on Lorentz violation in 21Ne are used to improve the limits on the Lorentz symmetry in the photon sector, namely the anisotropy of the speed of light and the Coulomb interactions, by 7 orders of magnitude in comparison with previous experiments: the speed of light is isotropic to a part in E-28.
On a Class of Feynman Integrals Evaluating to Iterated Integrals of Modular Forms
2019
In this talk we discuss a class of Feynman integrals, which can be expressed to all orders in the dimensional regularisation parameter as iterated integrals of modular forms. We review the mathematical prerequisites related to elliptic curves and modular forms. Feynman integrals, which evaluate to iterated integrals of modular forms go beyond the class of multiple polylogarithms. Nevertheless, we may bring for all examples considered the associated system of differential equations by a non-algebraic transformation to an \(\varepsilon \)-form, which makes a solution in terms of iterated integrals immediate.
Generation of minimum energy entangled states
2020
Quantum technologies exploiting bipartite entanglement could be made more efficient by using states having the minimum amount of energy for a given entanglement degree. Here, we study how to generate these states in the case of a bipartite system of arbitrary finite dimension either by applying a unitary transformation to its ground state or through a zero-temperature thermalization protocol based on turning on and off a suitable interaction term between the subsystems. In particular, we explicitly identify three possible unitary operators and five possible interaction terms. On the one hand, two of the three unitary transformations turn out to be easily decomposable in terms of local eleme…
Relaxation due to random collisions with a many-qudit environment
2008
We analyze the dynamics of a system qudit of dimension mu sequentially interacting with the nu-dimensional qudits of a chain playing the ore of an environment. Each pairwise collision has been modeled as a random unitary transformation. The relaxation to equilibrium of the purity of the system qudit, averaged over random collisions, is analytically computed by means of a Markov chain approach. In particular, we show that the steady state is the one corresponding to the steady state for random collisions with a single environment qudit of effective dimension nu_e=nu*mu. Finally, we numerically investigate aspects of the entanglement dynamics for qubits (mu=nu=2) and show that random unitary …
Limited preparation contextuality in quantum theory and its relation to the Cirel'son bound
2015
Kochen-Specker (KS) theorem lies at the heart of the foundations of quantum mechanics. It establishes impossibility of explaining predictions of quantum theory by any noncontextual ontological model. Spekkens generalized the notion of KS contextuality in [Phys. Rev. A 71, 052108 (2005)] for arbitrary experimental procedures (preparation, measurement, and transformation procedure). Interestingly, later on it was shown that preparation contextuality powers parity-oblivious multiplexing [Phys. Rev. Lett. 102, 010401 (2009)], a two party information theoretic game. Thus, using resources of a given operational theory, the maximum success probability achievable in such a game suffices as a \emph{…
From loops to trees by-passing Feynman's theorem
2008
We derive a duality relation between one-loop integrals and phase-space integrals emerging from them through single cuts. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators. The new prescription regularizing the propagators, which we write in a Lorentz covariant form, compensates for the absence of multiple-cut contributions that appear in the Feynman Tree Theorem. The duality relation can be applied to generic one-loop quantities in any relativistic, local and unitary field theories. %It is suitable for applications to the analytical calculation of %one-loop scattering amplitudes, and to the numerical evaluation of %cross-section…
Nonperturbative comparison of QCD effective charges
2009
We study the non-perturbative behavior of two versions of the QCD effective charge, one obtained from the pinch technique gluon self-energy, and one from the ghost-gluon vertex. Despite their distinct theoretical origin, due to a fundamental identity relating various of the ingredients appearing in their respective definitions, the two effective charges are almost identical in the entire range of physical momenta, and coincide exactly in the deep infrared, where they freeze at a common finite value. Specifically, the dressing function of the ghost propagator is related to the two form factors in the Lorentz decomposition of a certain Green's function, appearing in a variety of field-theoret…