Related papers: Some globally conserved currents from generalized …
Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard…
This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field…
The zero curvature representation of Zakharov and Shabat has been generalized recently to higher dimensions and has been used to construct non-linear field theories which either are integrable or contain integrable submodels. The Skyrme…
A very general class of Lagrangians which couple scalar fields to gravitation and matter in two spacetime dimensions is investigated. It is shown that a vector field exists along whose flow lines the stress-energy tensor is conserved,…
The creation of quantum coherences requires a system to be anharmonic. The simplest such continuous 1D quantum system is the Kerr oscillator. It has a number of interesting symmetries we derive. Its quantum dynamics is best studied in phase…
For every conserved quantity written as a sum of local terms, there exists a corresponding current operator that satisfies the continuity equation. The expectation values of current operators at equilibrium define the persistent currents…
By using conformal Killing-Yano tensors, and their generalisations, we obtain scalar potentials for both the source-free Maxwell and massless Dirac equations. For each of these equations we construct, from conformal Killing-Yano tensors,…
Employing a Mathematica symbolic computer algebra package called xTensor, we present $(1+3)$-covariant special case proofs of the shear-free perfect fluid conjecture in General Relativity. We first present the case where the pressure is…
We prove that any compact Cauchy horizon with constant non-zero surface gravity in a smooth vacuum spacetime is a smooth Killing horizon. The novelty here is that the Killing vector field is shown to exist on both sides of the horizon. This…
A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean space. This kernel is built using the reservoir…
We establish the existence of a deformation of the usual Carter constant which is conserved along the motion in a fixed Kerr background of a spinning test body possessing the spin-induced quadrupole coupling of a black hole. The…
Given a coherent ideal sheaf $J$ we construct locally a vector-valued residue current $R$ whose annihilator is precisely the given sheaf. In case $J$ is a complete intersection, $R$ is just the classical Coleff-Herrera product. By means of…
We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved spacetime with Killing vectors. This definition enables us to define energy and momentum for matter by the…
We extend the standard construction of conserved currents for matter fields in general relativity to general gauge theories. In the original construction the conserved current associated with a spacetime symmetry generated by a Killing…
Every Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fields (equivalently, every polynomial in the velocities…
The quantum effective action yields equations of motion and correlation functions including all quantum corrections. We discuss here how it encodes also Noether currents at the full quantum level. Interestingly, the construction can be…
We construct a planar smooth weakly mixing stationary random vector field with nonnegative components such that, with probability 1, the flow generated by this vector field does not have an asymptotic direction. Moreover, for all individual…
We construct an asymptotic conserved charge for a current that has been defined using Killing-Yano tensors. We then calculate the corresponding conserved charges of of the Kerr and AdS-Kerr black holes, and their higher-dimensional…
The electric current conservation in a two-dimensional quantum wire under a time dependent field is investigated. Such a conservation is obtained as the global density of states contribution to the emittance is balanced by the contribution…
Let $M$ be a locally rotationally symmetric spacetime, and $\xi^a$ a conformal Killing vector for the metric on $M$, lying in the subspace spanned by the unit timelike direction and the preferred spatial direction, and with non-constant…