SU(1,4) as a dynamical group; analysis of all the discrete representations. I. Baryons

1977 ◽  
Vol 55 (7-8) ◽  
pp. 673-676 ◽  
Author(s):  
C. S. Kalman
Keyword(s):  
Symmetry Group ◽  
Group Analysis ◽  
Dynamical Group ◽  
Charmed Baryons ◽  
Discrete Representations ◽  
The Masses

A method using SU(1,3) as a dynamical group for the baryons is extended to SU(1,4) by inclusion of the charm symmetry group SU(4) as maximum kinematic group. Several new mass formulae are given and the masses of the charmed baryons are predicted.

SU(1, 3) as a Dynamical Group; Analysis of All the Discrete Representations

1973 ◽  
Vol 51 (14) ◽  
pp. 1573-1576 ◽  
Author(s):  
C. S. Kalman
Keyword(s):  
Group Analysis ◽  
Strong Interactions ◽  
Dynamical Group ◽  
Physical Conditions ◽  
Degenerate Representation ◽  
Discrete Representations

A method using the most degenerate representation of SU(1, 3) as a dynamical group for the strong interactions of the spin 1/2+ baryons is extended to consider all the discrete representations. It is shown that physical conditions place very severe restrictions on the parameters characterizing such a representation.

scholarly journals Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Masatomo Iwasa
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Singular Perturbation ◽  
Symmetry Group ◽  
Group Analysis ◽  
Lie Symmetry ◽  
Symmetry Groups ◽  
Lie Group Analysis ◽  
Constraint Equations ◽  
Perturbation Problems

Lie group analysis has been applied to singular perturbation problems in both ordinary differential and difference equations and has allowed us to find the reduced dynamics describing the asymptotic behavior of the dynamical system. The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. This extension makes it possible to find a partial Lie symmetry group, which leads to a reduced dynamics describing the asymptotic behavior.

Masses of charmed baryons inSU 1,4 dynamical group theory

1980 ◽  
Vol 27 (15) ◽  
pp. 481-485 ◽  
Author(s):  
M. O’Neill ◽  
C. S. Kalman
Keyword(s):  
Group Theory ◽  
Dynamical Group ◽  
Charmed Baryons

Lie Symmetry Group of the Nonisospectral Kadomtsev-Petviashvili Equation

2009 ◽  
Vol 64 (1-2) ◽  
pp. 8-14 ◽  
Author(s):  
Yong Chen ◽  
Xiaorui Hu
Keyword(s):  
Symmetry Group ◽  
Discrete Group ◽  
Group Analysis ◽  
Lie Symmetry ◽  
Kp Equation ◽  
Classical Symmetry ◽  
Petviashvili Equation ◽  
Finite Transformation ◽  
Special Case ◽  
Symmetry Method

The classical symmetry method and the modified Clarkson and Kruskal (C-K) method are used to obtain the Lie symmetry group of a nonisospectral Kadomtsev-Petviashvili (KP) equation. It is shown that the Lie symmetry group obtained via the traditional Lie approach is only a special case of the symmetry groups obtained by the modified C-K method. The discrete group analysis is given to show the relations between the discrete group and parameters in the ansatz. Furthermore, the expressions of the exact finite transformation of the Lie groups via the modified C-K method are much simpler than those obtained via the standard approach.

q-ANALOGUE OF BOSON COMMUTATOR AND THE QUANTUM GROUPS SUq(2) AND SUq(1, 1)

1990 ◽  
Vol 05 (04) ◽  
pp. 237-242 ◽  
Author(s):  
HARUO UI ◽  
N. AIZAWA
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Group ◽  
Symmetry Group ◽  
Quantum Groups ◽  
Heisenberg Algebra ◽  
Positive Definiteness ◽  
Two Dimensional ◽  
Number Operator ◽  
Boson Operator ◽  
Dynamical Group

We propose a defining set of commutation relations to a q-analogue of boson operator; [Formula: see text], [Formula: see text] and [N, aq]=−aq, which contracts to the Heisenberg algebra of boson operators in the limit of q=1. Here, N is the number operator, [N]q being its q-analogue operator. By making use of this set, we construct a new realization of the “noncompact” quantum group SUq(1, 1) in addition to that of the SUq(2) recently proposed by Biedenharn. The explicit form of the number operator is given in terms of aq and [Formula: see text] and its positive definiteness is proved. A uniqueness of our commutators is also discussed. It is shown that the quantum group SUq(2) appears as a true symmetry group of a q-analogue of the two-dimensional harmonic oscillator and the SUq(1, 1) as its dynamical group.

PRELIMINARY GROUP ANALYSIS OF A 4 X 4 TWO DIMENSIONAL HUBBARD MODEL

1989 ◽  
Vol 03 (12) ◽  
pp. 1845-1852 ◽  
Author(s):  
G. Fano ◽  
F. Ortolani ◽  
F. Semeria
Keyword(s):  
Hubbard Model ◽  
Symmetry Group ◽  
High Speed ◽  
Group Analysis ◽  
Finite Size ◽  
Exact Diagonalization ◽  
Two Dimensional ◽  
Spatial Symmetry ◽  
Preliminary Group

A finite size two-dimensional Hubbard model is considered; it is shown that the consideration of the spatial symmetry group of the Hamiltonian reduces the dimension of the problem of two orders of magnitude in the case of a 4 X 4 lattice. Exact diagonalization of the Hamiltonian can then be performed with the aid of modern high-speed computers.

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