scholarly journals Spherical functions of the Lorentz group on the two dimensional complex sphere of zero radius

1971 ◽  
Vol 23 (2) ◽  
pp. 132-136 ◽  
Author(s):  
M. Huszár
Keyword(s):  
Lorentz Group ◽  
Spherical Functions ◽  
Two Dimensional ◽  
Complex Sphere ◽  
Zero Radius

Canonical representations for massless particles and zero-mass limits of the helicity representation

1965 ◽  
Vol 285 (1401) ◽  
pp. 287-296 ◽  
Keyword(s):  
Lorentz Group ◽  
Irreducible Representations ◽  
Two Dimensional ◽  
Euclidean Group ◽  
Positive Mass ◽  
Continuous Spin ◽  
Massless Particles ◽  
Zero Mass ◽  
Canonical Representations ◽  
Inhomogeneous Lorentz Group

The global forms of the unitary irreducible representations of the inhomogeneous Lorentz group corresponding to zero mass and finite or continuous spin are constructed by means of the little-group technique from those of the two-dimensional Euclidean group, and it is shown that these representations may be derived from the helicity representation for positive mass by taking suitable limits.

scholarly journals A CRITERION FOR THE UNIQUE SOLVABILITY OF THE POINCARE SPECTRAL PROBLEM IN A CYLINDRICAL DOMAIN FOR ONE CLASS OF MULTIDIMENSIONAL ELLIPTIC EQUATIONS

2019 ◽  
pp. 5-14
Author(s):  
S. A. Aldashev
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Unique Solvability ◽  
Elliptic Equations ◽  
Singular Integral Equations ◽  
Spherical Functions ◽  
Cylindrical Domain ◽  
Two Dimensional ◽  
Single Class ◽  
Poincaré Problem

Two-dimensional spectral problems for elliptic equations are well studied, and their multidimensional analogs, as far as the author knows, are little studied. This is due to the fact that in the case of three or more independent variables there are difficulties of a fundamental nature, since the method of singular integral equations, which is very attractive and convenient, used for two-dimensional problems, cannot be used here because of the lack of any complete theory of multidimensional singular integral equations. The theory of multidimensional spherical functions, on the contrary, has been adequately and fully studied. In the cylindrical domain of Euclidean space, for a single class of multidimensional elliptic equations, the spectral Poincare problem. The solution is sought in the form of an expansion in multidimensional spherical functions. The existence and uniqueness theorems of the solution are proved. Conditions for unique solvability of the problem are obtained, which essentially depend on the height of the cylinder.

scholarly journals MAXWELL FIELD ON THE POINCARÉ GROUP

2005 ◽  
Vol 20 (17) ◽  
pp. 4095-4112 ◽  
Author(s):  
V. V. VARLAMOV
Keyword(s):  
Maxwell Equations ◽  
Two Dimensional ◽  
Translation Group ◽  
Poincaré Group ◽  
Field Equations ◽  
Poincare Group ◽  
Massless Field ◽  
Complex Sphere ◽  
Maxwell Fields ◽  
Group Part

The massless field of spin 1 is defined on the eight-dimensional configuration space; this space is a direct product of Minkowski space and of a two-dimensional complex sphere. Field equations for the spin-one field are derived from a Dirac-like Lagrangian separately for the translation group and Lorentz group parts. It is shown that a Dirac form of Maxwell equations (the so-called Majorana–Oppenheimer formulation of electrodynamics) follows directly from the field equations of translation group part. The photon field is realized via Biedenharn type functions on the Poincaré group. This allows us to consider both Dirac and Maxwell fields on an equal footing, as the functions on the Poincaré group.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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