Search results for "REPRESENTATION"
showing 10 items of 1710 documents
Cohomology of Lie algebras
1995
This chapter is devoted to studying some concepts that will be extensively used in the last chapters, namely the cohomology of Lie algebras with values in a vector space, the Whitehead lemmas and Lie algebra extensions (which are related to second cohomology groups). The same three different cases of extensions of chapter 5 as well as the ℱ( M )-valued version of cohomology will be considered. In fact, the relation between Lie group and Lie algebra cohomology will be explored here, first with the simple example of central extensions of groups and algebras (governed by twococycles), and then in the higher order case, providing explicit formulae for obtaining Lie algebra cocycles from Lie gro…
GiNaC - Symbolic computation with C++
2005
We give an introduction to the C++ library GiNaC, which extends the C++ language by new objects and methods for the representation and manipulation of arbitrary symbolic expressions.
Solution for an arbitrary number of coupled identical oscillators.
1992
We propose a solution to the problem of solving the Schr\"odinger equation for an arbitrary number of identical one-dimensional harmonically coupled oscillators raised by Fan Hong-yi [Phys. Rev. A 42, 4377 (1990)]. The relationship between the Fock spaces associated with the uncoupled and coupled oscillators is given as well as the coordinate representation of the eigenstates. In view of further applications, the Lie algebraic properties of the model are examined, and the generalization to three spatial dimensions is made.
Free fields via canonical transformations of matter-coupled two-dimensional dilaton gravity models
1998
It is shown that the 1+1-dimensional matter-coupled Jackiw-Teitelboim model and the model with an exponential potential can be converted by means of appropriate canonical transformations into a bosonic string theory propagating on a flat target space with an indefinite signature. This makes it possible to consistently quantize these models in the functional Schroedinger representation thus generalizing recent results on CGHS theory.
Tenth Peregrine breather solution to the NLS equation
2015
We go on in this paper, in the study of the solutions of the focusing NLS equation. With a new representation given in a preceding paper, a very compact formulation without limit as a quotient of two determinants, we construct the Peregrine breather of order N=10. The explicit analytical expression of the Akhmediev's solution is completely given.
The electronic structure of N-methyl-3pyridone and its representation
1970
Quasi-localized MO's have been constructed for the π electron system of the three pyridone isomers.
Particle Plasmons as Dipole Antennas: State Representation of Relative Observables
2018
The strong interactions between light and plasmons (in metal nanoparticles) allow to observe chemical and physical processes on and around the particle on nanometer length scales as well as they al...
Illustration of microphysical processes in Amazonian deep convective clouds in the gamma phase space: introduction and potential applications
2017
Abstract. The behavior of tropical clouds remains a major open scientific question, resulting in poor representation by models. One challenge is to realistically reproduce cloud droplet size distributions (DSDs) and their evolution over time and space. Many applications, not limited to models, use the gamma function to represent DSDs. However, even though the statistical characteristics of the gamma parameters have been widely studied, there is almost no study dedicated to understanding the phase space of this function and the associated physics. This phase space can be defined by the three parameters that define the DSD intercept, shape, and curvature. Gamma phase space may provide a commo…
Nonparaxial shape-preserving Airy beams with Bessel signature
2014
Spatially accelerating beams that are solutions to Maxwell equations may propagate along incomplete circular trajectories. Taking these truncated Bessel fields to the paraxial limit, some authors have sustained that it has recovered the known Airy beams (AiBs). Based on the angular spectrum representation of optical fields, we demonstrated that the paraxial approximation rigorously leads to off-axis focused beams instead of finite-energy AiBs. The latter will arise under the umbrella of a nonparaxial approach following elliptical trajectories in place of parabolas. The analytical expression of such a shape-preserving wave field under Gaussian apodization is disclosed by using third-order no…
Two- and Three-Pion Finite-Volume Spectra at Maximal Isospin from Lattice QCD.
2019
We present the three-pion spectrum with maximal isospin in a finite volume determined from lattice QCD, including excited states in addition to the ground states across various irreducible representations at zero and nonzero total momentum. The required correlation functions, from which the spectrum is extracted, are computed using a newly implemented algorithm which speeds up the computation by more than an order of magnitude. On a subset of the data we extract a nonzero value of the three-pion threshold scattering amplitude using the $1/L$ expansion of the three-particle quantization condition, which consistently describes all states at zero total momentum. The finite-volume spectrum is p…