120,159 research outputs found
Space-time symplectic extension
It is conjectured that in the origin of space-time there lies a symplectic
rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1
instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the
space-time local structure group. A discrete sequence of the metric space-times
of the fixed dimensionalities d=(2l)^2 and signatures, with l(2l-1) time-like
and l(2l+1) space-like directions, defined over the set of the Hermitian
second-rank spin-tensors is considered as an alternative to the
pseudo-Euclidean extra dimensional space-times. The basic concepts of the
symplectic framework are developed in general, and the ordinary and
next-to-ordinary space-time cases with l=1,2, respectively, are elaborated in
more detail. In particular, the scheme provides the rationale for the
four-dimensionality and 1+3 signature of the ordinary space-time.Comment: 15 pp, LaTe
Accurate and efficient algorithm for Bader charge integration
We propose an efficient, accurate method to integrate the basins of
attraction of a smooth function defined on a general discrete grid, and apply
it to the Bader charge partitioning for the electron charge density. Starting
with the evolution of trajectories in space following the gradient of charge
density, we derive an expression for the fraction of space neighboring each
grid point that flows to its neighbors. This serves as the basis to compute the
fraction of each grid volume that belongs to a basin (Bader volume), and as a
weight for the discrete integration of functions over the Bader volume.
Compared with other grid-based algorithms, our approach is robust, more
computationally efficient with linear computational effort, accurate, and has
quadratic convergence. Moreover, it is straightforward to extend to non-uniform
grids, such as from a mesh-refinement approach, and can be used to both
identify basins of attraction of fixed points and integrate functions over the
basins.Comment: 19 pages, 8 figure
Conformal self-dual fields
Conformal self-dual fields in flat space-time of even dimension greater than
or equal to four are studied. Ordinary-derivative formulation of such fields is
developed. Gauge invariant Lagrangian with conventional kinetic terms and
corresponding gauge transformations are obtained. Gauge symmetries are realized
by involving the Stueckelberg fields. Realization of global conformal
symmetries is obtained. Light-cone gauge Lagrangian is found. Also, we
demonstrate use of the light-cone gauge for counting of on-shell degrees of
freedom of the conformal self-dual fields.Comment: 28 pages, LaTeX-2e, v3: Discussion of realization of conformal
algebra symmetries on field strengths added to Sections 3,5. Appendices B,C,D
and one reference added. Typos correcte
Synchro-curvature radiation of charged particles in the strong curved magnetic fields
It is generally believed that the radiation of relativistic particles in a
curved magnetic field proceeds in either the synchrotron or the curvature
radiation modes. In this paper we show that in strong curved magnetic fields a
significant fraction of the energy of relativistic electrons can be radiated
away in the intermediate, the so-called synchro-curvature regime. Because of
the persistent change of the trajectory curvature, the radiation varies with
the frequency of particle gyration. While this effect can be ignored in the
synchrotron and curvature regimes, the variability plays a key role in the
formation of the synchro-curvature radiation. Using the Hamiltonian formalism,
we find that the particle trajectory has the form of a helix wound around the
drift trajectory. This allows us to calculate analytically the intensity and
energy distribution of prompt radiation in the general case of magnetic
bremsstrahlung in the curved magnetic field. We show that the transition to the
limit of the synchrotron and curvature radiation regimes is determined by the
relation between the drift velocity and the component of the particle velocity
perpendicular to the drift trajectory. The detailed numerical calculations,
which take into account the energy losses of particles, confirm the principal
conclusions based on the simplified analytical treatment of the problem, and
allow us to analyze quantitatively the transition between different radiation
regimes for a broad range of initial pitch angles. We argue that in the case of
realization of specific configurations of the electric and magnetic fields, the
gamma-ray emission of the pulsar magnetospheres can be dominated by the
component radiated in the synchro-curvature regime.Comment: this article supersedes arXiv:1207.6903 and arXiv:1305.078
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