scholarly journals Internal Movement of Hadrons as Infinite-Dimensional Representation of Inner Lorentz Group

1967 ◽  
Vol 37 (4) ◽  
pp. 765-766 ◽  
Author(s):  
Takehiko Takabayasi
Keyword(s):  
Lorentz Group ◽  
Dimensional Representation ◽  
Infinite Dimensional ◽  
Infinite Dimensional Representation

QUASI-EXACTLY SOLVABLE PROBLEMS AND SU(1,1) GROUP

1994 ◽  
Vol 09 (16) ◽  
pp. 1501-1505 ◽  
Author(s):  
O.B. ZASLAVSKII
Keyword(s):  
Lie Algebra ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Infinite Dimensional ◽  
Exactly Solvable ◽  
Solvable Problems ◽  
Infinite Dimensional Representation

It is shown that the particular class of one-dimensional quasi-exactly solvable models can be constructed with the help of infinite-dimensional representation of Lie algebra. Hamiltonian of a system is expressed in terms of SU(1,1) generators.

COLORED BRAID MATRICES FROM INFINITE-DIMENSIONAL REPRESENTATIONS OF Uq(g)

1992 ◽  
Vol 07 (09) ◽  
pp. 767-779 ◽  
Author(s):  
TETSUO DEGUCHI ◽  
YASUHIRO AKUTSU
Keyword(s):  
Alexander Polynomial ◽  
Dimensional Representation ◽  
R Matrix ◽  
Infinite Dimensional ◽  
Vertex Models ◽  
Infinite Dimensional Representation

From a new infinite-dimensional representation of the universal R-matrix of [Formula: see text], we derive the colored braid matrices which gave generalizations of the multivariable Alexander polynomial. We propose color representations of Uq(g). We construct colored vertex models from the color representations of [Formula: see text].

Nonlinear Schrödinger Model with Boundary, Integrability and Scattering Matrix Based on the Degenerate Affine Hecke Algebra

1997 ◽  
Vol 12 (30) ◽  
pp. 5397-5410 ◽  
Author(s):  
Yasushi Komori ◽  
Kazuhiro Hikami
Keyword(s):  
Difference Operators ◽  
Baxter Equation ◽  
Many Body ◽  
Dimensional Representation ◽  
Systematic Method ◽  
Infinite Dimensional ◽  
Nonlinear Schrödinger ◽  
Scattering Matrices ◽  
Many Body Systems ◽  
Infinite Dimensional Representation

The δ-function interacting many-body systems (nonlinear Schrödinger models) on an infinite interval and with boundary are studied by use of the integrable differential-difference operators, so-called Dunkl operators. These models are related with the classical root systems of type A and BC, and we give a systematic method to construct these integrable operators. This method is based on the infinite-dimensional representation for solutions of the classical Yang–Baxter equation and the classical reflection equation. In addition the scattering matrices of the boundary nonlinear Schrödinger model are investigated.

Elements of Group Theory

2021 ◽  
pp. 51-110
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Group Theory ◽  
Lie Groups ◽  
Lorentz Group ◽  
Unitary Representations ◽  
Compact Groups ◽  
Mathematical Language ◽  
Group Representations ◽  
Infinite Groups ◽  
Infinite Dimensional ◽  
Symmetry Properties

The mathematical language which encodes the symmetry properties in physics is group theory. In this chapter we recall the main results. We introduce the concepts of finite and infinite groups, that of group representations and the Clebsch–Gordan decomposition. We study, in particular, Lie groups and Lie algebras and give the Cartan classification. Some simple examples include the groups U(1), SU(2) – and its connection to O(3) – and SU(3). We use the method of Young tableaux in order to find the properties of products of irreducible representations. Among the non-compact groups we focus on the Lorentz group, its relation with O(4) and SL(2,C), and its representations. We construct the space of physical states using the infinite-dimensional unitary representations of the Poincaré group.

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