scholarly journals Affine symmetry, geodesics, and homogeneous spacetimes

2018 ◽  
Vol 50 (8) ◽  
Author(s):  
David Maughan ◽  
Charles Torre
Keyword(s):  
Affine Symmetry

scholarly journals Quantum affine symmetry as generalized supersymmetry

1993 ◽  
Vol 401 (1-2) ◽  
pp. 413-454 ◽  
Author(s):  
André LeClair ◽  
Cumrun Vafa
Keyword(s):  
Affine Symmetry

THE AFFINE N = 4 YANG–MILLS THEORY

1992 ◽  
Vol 07 (11) ◽  
pp. 2469-2485
Author(s):  
A. C. CADAVID ◽  
R. J. FINKELSTEIN
Keyword(s):  
Mass Spectrum ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Effective Theory ◽  
Affine Algebra ◽  
Linear Mass ◽  
Expectation Value ◽  
Yang Mills ◽  
Exotic States ◽  
Affine Symmetry

An affine field theory may be constructed by gauging an affine algebra. The momentum integrals of the affine N = 4 Yang–Mills theory are ultraviolet finite but diverge because the sum over states is infinite. If the affine symmetry is broken by postulating a nonvanishing vacuum expectation value for that component of the scalar field lying in the L0 direction, then the theory acquires a linear mass spectrum. This broken theory is ultraviolet finite too, but the mass spectrum is unbounded. If it is also postulated that the mass spectrum has an upper bound (say, the Planck mass), then the resulting theory appears to be altogether finite. The influence of the exotic states has been estimated and, according to the proposed scenario, is negligible below energies at which gravitational interactions become important. The final effective theory has the symmetry of a compact Lie algebra augmented by the operator L0.

scholarly journals Affine symmetry in mechanics of collective and internal modes Part I. classical models

2004 ◽  
Vol 54 (3) ◽  
pp. 373-427 ◽  
Author(s):  
J.J. Sławianowski ◽  
V. Kovalchuk ◽  
A. Sławianowska ◽  
B. Gołubowska ◽  
A. Martens ◽  
...  
Keyword(s):  
Affine Symmetry ◽  
Classical Models

Affine Symmetry Semi-Groups for Quasi-Crystals

1994 ◽  
Vol 25 (6) ◽  
pp. 435-440 ◽  
Author(s):  
D Barache ◽  
S. de Bievre ◽  
J. P Gazeau
Keyword(s):  
Affine Symmetry ◽  
Quasi Crystals

scholarly journals Affine Symmetry Tensors in Minkowski Space

2016 ◽  
Vol 13 (3) ◽  
Author(s):  
Isaac Ahern ◽  
Sam Cook
Keyword(s):  
Minkowski Space ◽  
Computational Algorithm ◽  
Minkowski Spacetime ◽  
Lie Derivative ◽  
Killing Tensor ◽  
Spacetime Dimension ◽  
Killing Vectors ◽  
Killing Tensors ◽  
Affine Symmetry

Killing vectors are generators of symmetries in a spacetime. This article defines certain generalizations of Killing vectors, called affine symmetry tensors, or simply affine tensors. While the affine vectors of the Minkowski spacetime are well known, and partial results for valence n = 2 have been discussed, affine tensors of valence n > 2 have never been exhibited. In this article, we discuss a computational algorithm to compute affine tensors in Minkowski spacetime, and discuss the results for affine tensors of valence 2 ≤ n ≤ 7. After comparison with analogous results concerning Killing tensors, we make several conjectures about the spaces of affine tensors in Minkowski spacetime. KEYWORDS: Affine Symmetry Tensors; Affine Vectors; Killing Tensors; Killing Vectors; Minkowski Spacetime; Dimension; Maple CAS; Lie Derivative; Generalized Killing Tensor

scholarly journals QUANTUM AFFINE SYMMETRY IN VERTEX MODELS

1993 ◽  
Vol 08 (08) ◽  
pp. 1479-1511 ◽  
Author(s):  
MAKOTO IDZUMI ◽  
TETSUJI TOKIHIRO ◽  
KENJI IOHARA ◽  
MICHIO JIMBO ◽  
TETSUJI MIWA ◽  
...  
Keyword(s):  
Representation Theory ◽  
Tensor Product ◽  
Spin Chain ◽  
Vertex Model ◽  
Quantum Affine Algebra ◽  
Affine Algebra ◽  
Affine Symmetry ◽  
Higher Spin ◽  
Local Operators ◽  
The One

We study the higher spin analogs of the six-vertex model on the basis of its symmetry under the quantum affine algebra [Formula: see text]. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer matrix, vacuum, creation/ annihilation operators of particles, and local operators, purely in the language of representation theory. We find that, regardless of the level of the representation involved, the particles have spin 1/2, and that the n-particle space has an RSOS type structure rather than a simple tensor product of the one-particle space. This agrees with the picture proposed earlier by Reshetikhin.

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