Characterization of SU(1,1) coherent states in terms of affine group wavelets

The Perelomov coherent states of SU(1,1) are labeled by elements of the quotient of SU(1,1) by the compact subgroup. Taking advantage of the fact that this quotient is isomorphic to the affine group of the real line, we are able to parameterize the coherent states by elements of that group or equivalently by points in the half-plane. Such a formulation permits to find new properties of the SU(1,1) coherent states and to relate them to affine wavelets.Comment: 11 pages, latex, to be published in J. Phys. A : Math. Ge

There are no magnetically charged particle-like solutions of the Einstein Yang-Mills equations for Abelian models

We prove that there are no magnetically charged particle-like solutions for Abelian models in Einstein Yang-Mills, but for non-Abelian models the possibility remains open. An analysis of the Lie algebraic structure of the Yang-Mills fields is essential to our results. In one key step of our analysis we use invariant polynomials to determine which orbits of the gauge group contain the possible asymptotic Yang-Mills field configurations. Together with a new horizontal/vertical space decomposition of the Yang-Mills fields this enables us to overcome some obstacles and complete a dynamical system existence theorem for asymptotic solutions with nonzero total magnetic charge. We then prove that these solutions cannot be extended globally for Abelian models and begin an investigation of the details for non-Abelian models.Comment: 48 pages, 1 figur

A procedure for developing an acceptance test for airborne bathymetric lidar data application to NOAA charts in shallow waters

National Oceanic and Atmospheric Administration (NOAA) hydrographic data is typically acquired using sonar systems, with a small percent acquired via airborne lidar bathymetry for near‐shore areas. This study investigated an integrated approach for meeting NOAA’s hydrographic survey requirements for near‐shore areas of NOAA charts, using the existing topographic‐bathymetric lidar data from USACE’s National Coastal Mapping Program (NCMP). Because these existing NCMP bathymetric lidar datasets were not collected to NOAA hydrographic surveying standards, it is unclear if, and under what circumstances, they might aid in meeting certain hydrographic surveying requirements. The NCMP’s bathymetric lidar data are evaluated through a comparison to NOAA’s Office of Coast Survey hydrographic data derived from acoustic surveys. As a result, it is possible to assess if NCMP’s bathymetry can be used to fill in the data gap shoreward of the navigable area limit line (0 to 4 meters) and if there is potential for applying NCMP’s bathymetry lidar data to near‐shore areas deeper than 10 meters. Based on the study results, recommendations will be provided to NOAA for the site conditions where this data will provide the most benefit. Additionally, this analysis may allow the development of future operating procedures and workflows using other topographic‐ bathymetric lidar datasets to help update near‐shore areas of the NOAA charts

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe

Subnormal operators regarded as generalized observables and compound-system-type normal extension related to su(1,1)

In this paper, subnormal operators, not necessarily bounded, are discussed as generalized observables. In order to describe not only the information about the probability distribution of the output data of their measurement but also a framework of their implementations, we introduce a new concept compound-system-type normal extension, and we derive the compound-system-type normal extension of a subnormal operator, which is defined from an irreducible unitary representation of the algebra su(1,1). The squeezed states are characterized as the eigenvectors of an operator from this viewpoint, and the squeezed states in multi-particle systems are shown to be the eigenvectors of the adjoints of these subnormal operators under a representation. The affine coherent states are discussed in the same context, as well.Comment: LaTeX with iopart.cls, iopart12.clo, iopams.sty, The previous version has some mistake

Certified Computer Algebra on top of an Interactive Theorem Prover

Contains fulltext : 35027.pdf (publisher's version ) (Open Access