scholarly journals Spectral action in matrix form

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Ali H. Chamseddine ◽  
John Iliopoulos ◽  
Walter D. van Suijlekom
Keyword(s):  
Geometric Structure ◽  
Symmetry Algebra ◽  
Matrix Form ◽  
Spectral Action ◽  
Yang Mills ◽  
Euclidean Manifold ◽  
Component Form ◽  
Finite Space ◽  
Electroweak Model ◽  
Quantization Rules

AbstractQuantization of the noncommutative geometric spectral action has so far been performed on the final component form of the action where all traces over the Dirac matrices and symmetry algebra are carried out. In this work, in order to preserve the noncommutative geometric structure of the formalism, we derive the quantization rules for propagators and vertices in matrix form. We show that the results in the case of a product of a four-dimensional Euclidean manifold by a finite space, could be cast in the form of that of a Yang–Mills theory. We illustrate the procedure for the toy electroweak model.

"Conference on 60 Years of Yang-Mills Gauge Field Theories"

2015 ◽  
Vol 04 (01) ◽  
pp. 22-23
Author(s):  
Lars Brink
Keyword(s):  
Symmetry Algebra ◽  
Local Symmetry ◽  
Physical Review ◽  
Gauge Field Theories ◽  
Strong Interactions ◽  
Prototype Model ◽  
Yang Mills ◽  
Vector Bosons ◽  
In The Beginning ◽  
Chen Ning Yang

In 1954 Prof. Chen Ning Yang spent some time at Brookhaven National Laboratories where he met Robert Mills. They decided to study an extension of Quantum Electro Dynamics, where the local symmetry, the gauge symmetry, was a non-abelian symmetry algebra, SU(2), with three vector bosons mediating the forces between a doublet of matter particles. The symmetry that the authors had in mind was the isotopic symmetry and hence this was a prototype model for the strong interactions between protons and neutrons. The mass of the vector bosons was zero classically and the authors speculated that that they might obtain masses during quantization. On 1 October 1954 the Yang-Mills paper was published in the Physical Review. It was criticized directly by Wolfgang Pauli and others who argued that the vector particles would be massless leading to long-range interactions that was in contradiction to the experimental facts about the strong interactions. The interest in the paper was not so strong in the beginning.

scholarly journals ISOSPIN PARTICLE ON S2 WITH ARBITRARY NUMBER OF SUPERSYMMETRIES

2007 ◽  
Vol 22 (20) ◽  
pp. 1481-1492 ◽  
Author(s):  
SOON-TAE HONG ◽  
JOOHAN LEE ◽  
TAE HOON LEE ◽  
PHILLIAL OH
Keyword(s):  
Quantum Mechanics ◽  
Gauge Field ◽  
Arbitrary Number ◽  
Symmetry Algebra ◽  
Energy Spectra ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Isospin State ◽  
Specific Choice ◽  
Exact Energy

We study the supersymmetric quantum mechanics of an isospin particle in the background of spherically symmetric Yang–Mills gauge field. We show that on S2 the number of supersymmetries can be made arbitrarily large for a specific choice of the spherically symmetric SU (2) gauge field. However, the symmetry algebra containing the supercharges becomes nonlinear if the number of fermions is greater than two. We present the exact energy spectra and eigenfunctions, which can be written as the product of monopole harmonics and a certain isospin state. We also find that the supersymmetry is spontaneously broken if the number of supersymmetries is even.

Hidden-symmetry algebra for the self-dual Yang-Mills equation

1983 ◽  
Vol 121 (6) ◽  
pp. 391-396 ◽  
Author(s):  
Ling-Lie Chau ◽  
Ge Mo-Lin ◽  
A. Sinha ◽  
Wu Yong-Shi
Keyword(s):  
Symmetry Algebra ◽  
The Self ◽  
Yang Mills ◽  
Hidden Symmetry

INTERACTING INSTANTONS FOR TeV PHYSICS

1992 ◽  
Vol 07 (12) ◽  
pp. 2741-2773 ◽  
Author(s):  
HIDEAKI AOYAMA ◽  
HISASHI KIKUCHI
Keyword(s):  
Cross Section ◽  
Lepton Number ◽  
Higgs Model ◽  
Effective Theory ◽  
Quantum Mechanical ◽  
Yang Mills ◽  
Lepton Number Violation ◽  
Instanton Effect ◽  
Electroweak Model ◽  
Lepton Number Violating

Multi-instanton effect in the standard electroweak model for baryon and lepton number violation is discussed. Instanton interaction is shown to play a major role in the TeV range. First, the validity of the treatment of the interaction is explicitly checked in the quantum-mechanical case. Then interactions induced by both bosons and fermons are examined in the SU(2) Yang–Mills–Higgs model. They are shown to lead to an effective theory which is manifestly unitary. This results in an estimate that the relevant cross section saturates the unitary bound at the TeV scale, indicating the possibility of detecting baryon- and lepton-number-violating phenomena.

scholarly journals Explicit homogenized equations of the piezoelectricity theory in a two-dimensional domain with a very rough interface of comb-type

2013 ◽  
Vol 35 (1) ◽  
pp. 93-101
Author(s):  
Pham Chi Vinh ◽  
Do Xuan Tung
Keyword(s):  
Piezoelectric Materials ◽  
Continuity Condition ◽  
Matrix Form ◽  
Two Dimensional ◽  
Rough Interface ◽  
Component Form ◽  
Tetragonal Crystals ◽  
Linear Piezoelectricity ◽  
Basic Equations ◽  
Special Case

The main purpose of this paper is to derive explicit homogenized equations of the linear piezoelectricity in two-dimensional domains separated by a very rough interface of comb-type. In order to do that, first, the basic equations of the theory of piezoelectricity are written down in matrix form. Then, following the techniques presented recently by these authors, the explicit homogenized equation in matrix form and the associated continuity condition, for generally anisotropic piezoelectric materials, are derived. They are then written down in component form for a special case when the solids are made of tetragonal crystals of class 42m. Since the obtained equations are totally explicit, they are significant in use.

Geometry of the SU (2) Di-Meron Solution

1986 ◽  
Vol 41 (4) ◽  
pp. 571-584
Author(s):  
R. Brucker ◽  
M. Sorg
Keyword(s):  
Symmetric Space ◽  
Geometric Structure ◽  
Analytic Form ◽  
Riemannian Structure ◽  
Conformally Flat ◽  
Geometric Properties ◽  
Yang Mills ◽  
Locally Symmetric Space ◽  
Meron Solution

The geometric properties of the di-m eron solution to the SU (2) Yang-Mills equations are studied in detail. The essential geometric structure of this solution is that of a locally symmetric space endowed with a Riemannian structure which is conformally flat. The di-meron solution is representable by an integrable 3-distribution over Euclidean 4-space. The corresponding integral surfaces are obtained in analytic form.

scholarly journals The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang–Mills theory on a Minkowskian background

2020 ◽  
Vol 17 (08) ◽  
pp. 2050114
Author(s):  
Luca Accornero ◽  
Marcella Palese
Keyword(s):  
Field Theory ◽  
Geometric Structure ◽  
Arbitrary Order ◽  
Higher Order ◽  
Second Variation ◽  
Jacobi Fields ◽  
Yang Mills ◽  
Conserved Current ◽  
The Second Variation ◽  
Higher Order Lagrangian

We characterize the second variation of an higher order Lagrangian by a Jacobi morphism and by currents strictly related to the geometric structure of the variational problem. We discuss the relation between the Jacobi morphism and the Hessian at an arbitrary order. Furthermore, we prove that a pair of Jacobi fields always generates a (weakly) conserved current. An explicit example is provided for a Yang–Mills theory on a Minkowskian background.

scholarly journals Charge algebra for non-abelian large gauge symmetries at O(r)

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Miguel Campiglia ◽  
Javier Peraza
Keyword(s):  
Symplectic Structure ◽  
Gauge Theories ◽  
Symmetry Algebra ◽  
Tree Level ◽  
Null Infinity ◽  
Asymptotic Field ◽  
Yang Mills ◽  
Extended Space ◽  
Gauge Symmetries ◽  
Asymptotic Symmetries

Abstract Asymptotic symmetries of gauge theories are known to encode infrared properties of radiative fields. In the context of tree-level Yang-Mills theory, the leading soft behavior of gluons is captured by large gauge symmetries with parameters that are O(1) in the large r expansion towards null infinity. This relation can be extended to subleading order provided one allows for large gauge symmetries with O(r) gauge parameters. The latter, however, violate standard asymptotic field fall-offs and thus their interpretation has remained incomplete. We improve on this situation by presenting a relaxation of the standard asymptotic field behavior that is compatible with O(r) gauge symmetries at linearized level. We show the extended space admits a symplectic structure on which O(1) and O(r) charges are well defined and such that their Poisson brackets reproduce the corresponding symmetry algebra.

Geometric structure of N=1, D=10 and N=4, D=4 super Yang-Mills theory

1982 ◽  
Vol 196 (2) ◽  
pp. 205-239 ◽  
Author(s):  
R. D'Auria ◽  
P. Fré ◽  
A.J. Da Silva
Keyword(s):  
Geometric Structure ◽  
Yang Mills ◽  
Super Yang Mills Theory
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