Generalized chiral symmetry groups and the classification of hadrons

1969 ◽  
Vol 26 (1-2) ◽  
pp. 127-137
Author(s):  
F. Gürsey
Keyword(s):  
Chiral Symmetry ◽  
Symmetry Groups

scholarly journals CLASSIFICATION OF SYMMETRY GROUPS FOR PLANAR -BODY CHOREOGRAPHIES

2013 ◽  
Vol 1 ◽  
Author(s):  
JAMES MONTALDI ◽  
KATRINA STECKLES
Keyword(s):  
Braid Group ◽  
Connected Components ◽  
Symmetry Groups ◽  
Exceptional Groups ◽  
Strong Force ◽  
Symmetry Properties ◽  
Foundational Work ◽  
Force Potential ◽  
Planar Body

AbstractSince the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the $n$-body problem: periodic motions where the $n$ bodies all follow one another at regular intervals along a closed path. The principal approach combines variational methods with symmetry properties. In this paper, we give a systematic treatment of the symmetry aspect. In the first part, we classify all possible symmetry groups of planar $n$-body collision-free choreographies. These symmetry groups fall into two infinite families and, if $n$ is odd, three exceptional groups. In the second part, we develop the equivariant fundamental group and use it to determine the topology of the space of loops with a given symmetry, which we show is related to certain cosets of the pure braid group in the full braid group, and to centralizers of elements of the corresponding coset. In particular, we refine the symmetry classification by classifying the connected components of the set of loops with any given symmetry. This leads to the existence of many new choreographies in $n$-body systems governed by a strong force potential.

Noether symmetries of vacuum classes of pp-waves and the wave equation

2016 ◽  
Vol 13 (09) ◽  
pp. 1650109 ◽  
Author(s):  
Sameerah Jamal ◽  
Ghulam Shabbir
Keyword(s):  
Wave Equation ◽  
Gravitational Waves ◽  
Wave Equations ◽  
Noether Symmetry ◽  
Symmetry Groups ◽  
Noether Symmetries ◽  
Noether’S Theorem ◽  
Metric Functions ◽  
Symmetry Algebras

The Noether symmetry algebras admitted by wave equations on plane-fronted gravitational waves with parallel rays are determined. We apply the classification of different metric functions to determine generators for the wave equation, and also adopt Noether's theorem to derive conserved forms. For the possible cases considered, there exist symmetry groups with dimensions two, three, five, six and eight. These symmetry groups contain the homothetic symmetries of the spacetime.

Molecular Rovibronic Symmetries in Electric and Magnetic Fields

1975 ◽  
Vol 53 (19) ◽  
pp. 2210-2220 ◽  
Author(s):  
James K. G. Watson
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Field ◽  
Symmetry Groups ◽  
Nuclear Spins ◽  
Symmetry Classification ◽  
Electric And Magnetic Fields ◽  
Field Symmetry ◽  
Point Groups

The structures of the symmetry groups for the rovibronic levels of a molecule in a homogeneous electric or magnetic field are derived, and the symmetry classification of the levels in terms of the representations and corepresentations of these groups is discussed. Specific results are given for molecules of the point groups C3, C2v, C3v, D2d, and Td in an electric field. Symmetry in combined electric and magnetic fields and the inclusion of nuclear spins are considered briefly.

A Classification of the Possible Symmetry Groups of Liquid Crystals

1975 ◽  
Vol 31 (1-2) ◽  
pp. 171-184 ◽  
Author(s):  
S. Goshen ◽  
D. Mukamel ◽  
S. Shtrikman
Keyword(s):  
Liquid Crystals ◽  
Symmetry Groups

scholarly journals Classification of symmetry groups

1961 ◽  
Vol 14 (12) ◽  
pp. 1236-1242 ◽  
Author(s):  
W. T. Holser
Keyword(s):  
Symmetry Groups

Lie subgroups of symmetry groups of fluid dynamics and magnetohydro-dynamics equations

1995 ◽  
Vol 73 (7-8) ◽  
pp. 463-477 ◽  
Author(s):  
A. M. Grundland ◽  
L. Lalague
Keyword(s):  
Fluid Dynamics ◽  
Symmetry Algebra ◽  
Symmetry Groups ◽  
Systems Of Equations ◽  
Magnetohydrodynamics Equations ◽  
Infinite Dimensional ◽  
Isentropic Flow ◽  
Fluid Dynamics Equations ◽  
Symmetry Algebras

We classify the subalgebras of the symmetry algebras of fluid dynamics and magnetohydrodynamics equations into conjugacy classes under their respective groups. Both systems of equations are invariant under a Galilean-similitude algebra. In the case of the fluid dynamics equations, when the adiabatic exponent γ = 5/3, the symmetry algebra widens to a Galilean-projective algebra. We extend our previous classification of the symmetry algebra in the case of a nonstationary and isentropic flow to the general case of fluid dynamics and magnetohydrodynamics equations in (3 + 1) dimensions. The representatives of these algebras are given in normalized lists and presented in tables. Examples of invariant and partially invariant solutions, for both systems, are computed from representatives of these classifications. The final part of this work contains an analysis of this classification in connection with a further classification of the symmetry algebras in the case of the equations describing the flow of perfect gases. An explicit solution, in terms of Riemann invariants, is constructed from infinite-dimensional subalgebras of the symmetry algebra of the magnetohydrodynamics equations in the (1 + 2)-dimensional case.

Introduction

2012 ◽  
Author(s):  
Mark Green ◽  
Phillip Griffiths ◽  
Matt Kerr
Keyword(s):  
Lie Group ◽  
Hodge Structure ◽  
Algebraic Groups ◽  
Complex Multiplication ◽  
Symmetry Groups ◽  
Hodge Structures ◽  
Fundamental Symmetry ◽  
Variation Of Hodge Structure ◽  
Geometric Origin

This book deals with Mumford-Tate groups, the fundamental symmetry groups in Hodge theory. Much, if not most, of the use of Mumford-Tate groups has been in the study of polarized Hodge structures of level one and those constructed from this case. In this book, Mumford-Tate groups M will be reductive algebraic groups over ℚ such that the derived or adjoint subgroup of the associated real Lie group M ℝ contains a compact maximal torus. In order to keep the statements of the results as simple as possible, the book emphasizes the case when M ℝ itself is semi-simple. The discussion covers period domains and Mumford-Tate domains, the Mumford-Tate group of a variation of Hodge structure, Hodge representations and Hodge domains, Hodge structures with complex multiplication, arithmetic aspects of Mumford-Tate domains, classification of Mumford-Tate subdomains, and arithmetic of period maps of geometric origin.

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