SYMMETRY GROUPS OF THE MIC-KEPLER PROBLEM AND THEIR UNITARY REPRESENTATIONS

1993 ◽  
Author(s):  
TOSHIHIRO IWAI ◽  
YOSHIO UWANO
Keyword(s):  
Kepler Problem ◽  
Unitary Representations ◽  
Symmetry Groups

Relativistic extension of non-compact symmetry groups

1966 ◽  
Vol 289 (1417) ◽  
pp. 177-191 ◽  
Keyword(s):  
Symmetry Group ◽  
Conventional Method ◽  
Space Time ◽  
Unitary Representations ◽  
Symmetry Groups ◽  
Infinite Dimensional ◽  
Induced Representations ◽  
Relativistic Extension ◽  
A Chain

The problem of relativistieally boosting the unitary representations of a non-compact spin-containing rest-symmetry group is solved by starting with non-unitary infinite-dimensional representations of a relativistic extension of this group, by adjoining to this extension four space-time translations and by the napplying Bargmann-Wigner equations to guarantee aunitary norm. The procedure has similarities to the conventional method of induced representations. The boosting problem considered here is the first step towards the solution of the problem of coupling of such infinite-dimensional representations which is also briefly investigated. Startin g from a rest-symmetry like U (6,6) a chain of subgroups GL (6), U (3,3), etc., is exhibited for collinear and coplanar processes, etc.

Conserved quantities and symmetry groups for the Kepler problem

1967 ◽  
Vol 50 (1) ◽  
pp. 95-105 ◽  
Author(s):  
A. Simoni ◽  
B. Vitale ◽  
F. Zaccaria
Keyword(s):  
Kepler Problem ◽  
Symmetry Groups ◽  
Conserved Quantities

Dynamical and symmetry groups of the SU(2) Kepler problem

2000 ◽  
Vol 33 (3-4) ◽  
pp. 326-355 ◽  
Author(s):  
Toshihiro Iwai ◽  
Takehiko Sunako
Keyword(s):  
Kepler Problem ◽  
Symmetry Groups

scholarly journals To the 150th anniversary of the creation of the Periodic system of elements

2019 ◽  
Vol 55 (2) ◽  
pp. 242-254
Author(s):  
A. L. Gurskii ◽  
L. I. Hursky
Keyword(s):  
Periodic System ◽  
Mathematical Description ◽  
Modern Science ◽  
Unitary Representations ◽  
Symmetry Groups ◽  
Dynamic Symmetry ◽  
Infinite Dimensional ◽  
Quantum Numbers ◽  
Finite Dimensional ◽  
Periodic Law

The results of the discovery of the Periodic law by D. I. Mendeleev are considered, and the actual formulation of this law is given. Some examples of the use of symmetry groups in modern science are given. It is shown that the SO(4,2) group allows presenting the contents of the Periodic system of elements in full coincidence with the experimentally established structure of electronic shells of corresponding atoms without involving any additional quantum numbers characterizing the properties of atoms. adynamic substantiation of the use of representations of the dynamic symmetry group of the quantum system, isovalent to hydrogen, for a mathematical description of the properties of the symmetry of the Periodic system of elements is proposed. Using it, the splitting of the infinite-dimensional unitary representations of the group SO(4,2) into the finite-dimensional multiplets, determined by the quantum numbers describing the states of electrons, was implemented. A problem of inclusion of isotopes of elements in the Periodic system of elements is discussed.

scholarly journals Defect CFT techniques in the 6d $$ \mathcal{N} $$ = (2, 0) theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nadav Drukker ◽  
Malte Probst ◽  
Maxime Trépanier
Keyword(s):  
Stress Tensor ◽  
Unitary Representations ◽  
Point Function ◽  
Displacement Operator ◽  
Expectation Value ◽  
Operator Expansion ◽  
Bulk Stress ◽  
Defect Operator ◽  
Tensor Multiplet

Abstract Surface operators are among the most important observables of the 6d $$ \mathcal{N} $$ N = (2, 0) theory. Here we apply the tools of defect CFT to study local operator insertions into the 1/2-BPS plane. We first relate the 2-point function of the displacement operator to the expectation value of the bulk stress tensor and translate this relation into a constraint on the anomaly coefficients associated with the defect. Secondly, we study the defect operator expansion of the stress tensor multiplet and identify several new operators of the defect CFT. Technical results derived along the way include the explicit supersymmetry tranformations of the stress tensor multiplet and the classification of unitary representations of the superconformal algebra preserved by the defect.

scholarly journals Heterotic line bundle models on generalized complete intersection Calabi Yau manifolds

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Magdalena Larfors ◽  
Davide Passaro ◽  
Robin Schneider
Keyword(s):  
Line Bundle ◽  
Complete Intersection ◽  
Particle Physics ◽  
Model Building ◽  
Wilson Line ◽  
Symmetry Groups ◽  
The Standard Model ◽  
Order Of Magnitude ◽  
Systematic Program ◽  
Calabi Yau Manifolds

Abstract The systematic program of heterotic line bundle model building has resulted in a wealth of standard-like models (SLM) for particle physics. In this paper, we continue this work in the setting of generalised Complete Intersection Calabi Yau (gCICY) manifolds. Using the gCICYs constructed in ref. [1], we identify two geometries that, when combined with line bundle sums, are directly suitable for heterotic GUT models. We then show that these gCICYs admit freely acting ℤ2 symmetry groups, and are thus amenable to Wilson line breaking of the GUT gauge group to that of the standard model. We proceed to a systematic scan over line bundle sums over these geometries, that result in 99 and 33 SLMs, respectively. For the first class of models, our results may be compared to line bundle models on homotopically equivalent Complete Intersection Calabi Yau manifolds. This shows that the number of realistic configurations is of the same order of magnitude.

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