Infinite Discrete Symmetry Group for the Yang-Baxter Equations and their Higher Dimensional Generalizations

1993 ◽  
pp. 277-310
Author(s):  
M. Bellon ◽  
J.-M. Maillard ◽  
C. Viallet
Keyword(s):  
Symmetry Group ◽  
Discrete Symmetry ◽  
Higher Dimensional

scholarly journals Construction and Characterization of Representations of SU(7) for GUT Model Builders

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1044
Author(s):  
Daniel Jones ◽  
Jeffery A. Secrest
Keyword(s):  
Gauge Symmetry ◽  
Symmetry Group ◽  
Lie Group ◽  
Cartan Subalgebra ◽  
Natural Extension ◽  
Grand Unification ◽  
Raising And Lowering Operators ◽  
Higher Dimensional ◽  
Lowering Operators

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

Infinite discrete symmetry group for the Yang-Baxter equations: Spin models

1991 ◽  
Vol 157 (6-7) ◽  
pp. 343-353 ◽  
Author(s):  
M.P. Bellon ◽  
J.-M. Maillard ◽  
C.-M. Viallet
Keyword(s):  
Symmetry Group ◽  
Discrete Symmetry ◽  
Spin Models

scholarly journals A discrete symmetry group for maximal atmospheric neutrino mixing

2003 ◽  
Vol 572 (3-4) ◽  
pp. 189-195 ◽  
Author(s):  
Walter Grimus ◽  
Luı́s Lavoura
Keyword(s):  
Symmetry Group ◽  
Atmospheric Neutrino ◽  
Discrete Symmetry ◽  
Neutrino Mixing

scholarly journals A guide to lifting aperiodic structures

2016 ◽  
Vol 231 (9) ◽  
Author(s):  
Michael Baake ◽  
David Écija ◽  
Uwe Grimm
Keyword(s):  
Number Theory ◽  
Symmetry Group ◽  
Dimensional Space ◽  
A Priori ◽  
Physical Space ◽  
Explicit Methods ◽  
Natural Choice ◽  
Higher Dimensional ◽  
Crystallographic Symmetry ◽  
Point Set

AbstractThe embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a priori construction of a lattice in relation to a given symmetry group. Instead, some elementary properties of the point set in physical space are used, and explicit methods are described. This approach works particularly well for the standard symmetries encountered in the practical study of quasicrystalline phases. We also demonstrate this with a recent experimental example, taken from a sample with square-triangle tiling structure and (approximate) 12-fold symmetry.

scholarly journals Finite-size corrections in critical symmetry-resolved entanglement

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Benoit Estienne ◽  
Yacine Ikhlef ◽  
Alexi Morin-Duchesne
Keyword(s):  
Symmetry Group ◽  
Crucial Role ◽  
Entanglement Entropy ◽  
Scaling Limit ◽  
Finite Size ◽  
Discrete Symmetry ◽  
System Size ◽  
Quantum Systems ◽  
Finite Size Corrections

In the presence of a conserved quantity, symmetry-resolved entanglement entropies are a refinement of the usual notion of entanglement entropy of a subsystem. For critical 1d quantum systems, it was recently shown in various contexts that these quantities generally obey entropy equipartition in the scaling limit, i.e. they become independent of the symmetry sector. In this paper, we examine the finite-size corrections to the entropy equipartition phenomenon, and show that the nature of the symmetry group plays a crucial role. In the case of a discrete symmetry group, the corrections decay algebraically with system size, with exponents related to the operators' scaling dimensions. In contrast, in the case of a U(1) symmetry group, the corrections only decay logarithmically with system size, with model-dependent prefactors. We show that the determination of these prefactors boils down to the computation of twisted overlaps.

scholarly journals PT -symmetric quantum electrodynamics and unitarity

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120057 ◽  
Author(s):  
Kimball A Milton ◽  
E. K. Abalo ◽  
Prachi Parashar ◽  
Nima Pourtolami ◽  
J. Wagner
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Quantum Electrodynamics ◽  
Discrete Symmetry ◽  
New Approach ◽  
Higher Dimensional ◽  
The Status ◽  
Symmetric Quantum ◽  
Quantum Mechanical Systems ◽  
Invariant Quantum

More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, . It was shown that, if is unbroken, energies were, in fact, positive, and unitarity was satisfied. Since quantum mechanics is quantum field theory in one dimension—time—it was natural to extend this idea to higher-dimensional field theory, and in fact an apparently viable version of -invariant quantum electrodynamics (QED) was proposed. However, it has proved difficult to establish that the unitarity of the scattering matrix, for example, the Källén spectral representation for the photon propagator, can be maintained in this theory. This has led to questions of whether, in fact, even quantum mechanical systems are consistent with probability conservation when Green’s functions are examined, since the latter have to possess physical requirements of analyticity. The status of QED will be reviewed in this paper, as well as the general issue of unitarity.

On the discrete symmetry group of Narain orbifolds

1992 ◽  
Vol 275 (1-2) ◽  
pp. 47-54 ◽  
Author(s):  
Michał Spaliński
Keyword(s):  
Symmetry Group ◽  
Discrete Symmetry

Infinite discrete symmetry group for the Yang-Baxter equations. Vertex models

1991 ◽  
Vol 260 (1-2) ◽  
pp. 87-100 ◽  
Author(s):  
M.P. Bellon ◽  
J.-M. Maillard ◽  
C. Viallet
Keyword(s):  
Symmetry Group ◽  
Discrete Symmetry ◽  
Vertex Models
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