Generic points and invariant theory

1988 ◽  
pp. 73-92
Author(s):  
Winfried Bruns ◽  
Udo Vetter
Keyword(s):  
Invariant Theory ◽  
Generic Points

Scale-Invariant Theory of Optical Properties of Fractal Clusters

1990 ◽  
Author(s):  
Vadim A. Markel ◽  
Leonid S. Muratov ◽  
Mark I. Stockman ◽  
Thomas F. George
Keyword(s):  
Optical Properties ◽  
Invariant Theory ◽  
Scale Invariant ◽  
Fractal Clusters

The Standard Theory

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Gauge Theory ◽  
Invariant Theory ◽  
Standard Theory ◽  
Strong Interactions ◽  
Gauge Invariant ◽  
Electromagnetic Interactions ◽  
Protons And Neutrons ◽  
Free Particles ◽  
Theoretical Predictions ◽  
Theory And Experiment

All ingredients of the previous chapters are combined in order to build a gauge invariant theory of the interactions among the elementary particles. We start with a unified model of the weak and the electromagnetic interactions. The gauge symmetry is spontaneously broken through the BEH mechanism and we identify the resulting BEH boson. Then we describe the theory known as quantum chromodynamics (QCD), a gauge theory of the strong interactions. We present the property of confinement which explains why the quarks and the gluons cannot be extracted out of the protons and neutrons to form free particles. The last section contains a comparison of the theoretical predictions based on this theory with the experimental results. The agreement between theory and experiment is spectacular.

scholarly journals CONSTRUCTIVE NONCOMMMUTATIVE INVARIANT THEORY

2021 ◽  
Author(s):  
MÁTYÁS DOMOKOS ◽  
VESSELIN DRENSKY
Keyword(s):  
Lie Algebra ◽  
Associative Algebra ◽  
Invariant Theory ◽  
Reductive Group ◽  
Symmetric Tensor ◽  
Free Associative Algebra ◽  
Tensor Algebra ◽  
Enveloping Algebra ◽  
Finite Dimensional ◽  
Degree Bounds

AbstractThe problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite-dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same group acting on the symmetric tensor algebra of the Lie algebra. This process is applied to prove a constructive Hilbert–Nagata Theorem (including degree bounds) for the algebra of invariants in a Lie nilpotent relatively free associative algebra endowed with an action induced by a representation of a reductive group.

Agricultural Multifunctionality and Care Farming: Insight from the UK

2015 ◽  
Vol 4 (1) ◽  
pp. 74-86
Author(s):  
Paul Custance ◽  
Keith Walley ◽  
Gaynor Tate ◽  
Goksel Armagan
Keyword(s):  
Learning Material ◽  
Multifunctional Agriculture ◽  
Economic Support ◽  
International Audience ◽  
The Uk ◽  
Generic Points ◽  
Care Farming ◽  
Compare And Contrast ◽  
Insight Into

The purpose of the article is to provide insight into care farming and the role that it may play in agriltural multifunctionality. The paper outlines three case studies of care farming in the UK to compare and contrast the roles that such organizations may play in multifunctional agriculture. Although the work has the obvious limitation of being based on case-study care farms that are based in the UK, the findings are sufficiently generic to serve as valuable learning material for those interested in the subject and located anywhere in the world. The main finding from this study is that care farming can take many different forms but still contribute to agricultural multifunctionality. The study also confirms the important roles that economic support and favourable legislation play in successful care farming. The paper concludes that care farming is a legitimate form of agricultural multifunctionality but reminds those interested in setting up or promoting care farms of the need for a supportive economic and legislative environment. The paper provides contemporary insight into the concept of care farming as a form of agricultural multifunctionality. A number of generic points are made that should be of value to an international audience of academics researching in this area as well as students studying care farming and agricultural multifunctionality, farmers considering diversifying into care farming and politicians working to create a political and economic environment that may support care farms.

scholarly journals PERIODIC AUTOMORPHISMS, COMPATIBLE POISSON BRACKETS, AND GAUDIN SUBALGEBRAS

2021 ◽  
Author(s):  
DMITRI I. PANYUSHEV ◽  
OKSANA S. YAKIMOVA
Keyword(s):  
Poisson Bracket ◽  
Lie Algebra ◽  
Invariant Theory ◽  
Cyclic Permutation ◽  
Poisson Brackets ◽  
Enveloping Algebra ◽  
Order Automorphism ◽  
Finite Dimensional ◽  
Compatible Poisson Brackets ◽  
Commutative Subalgebras

AbstractLet 𝔮 be a finite-dimensional Lie algebra. The symmetric algebra (𝔮) is equipped with the standard Lie–Poisson bracket. In this paper, we elaborate on a surprising observation that one naturally associates the second compatible Poisson bracket on (𝔮) to any finite order automorphism ϑ of 𝔮. We study related Poisson-commutative subalgebras (𝔮; ϑ) of 𝒮(𝔮) and associated Lie algebra contractions of 𝔮. To obtain substantial results, we have to assume that 𝔮 = 𝔤 is semisimple. Then we can use Vinberg’s theory of ϑ-groups and the machinery of Invariant Theory.If 𝔤 = 𝔥⊕⋯⊕𝔥 (sum of k copies), where 𝔥 is simple, and ϑ is the cyclic permutation, then we prove that the corresponding Poisson-commutative subalgebra (𝔮; ϑ) is polynomial and maximal. Furthermore, we quantise this (𝔤; ϑ) using a Gaudin subalgebra in the enveloping algebra 𝒰(𝔤).

TREE DIAGRAMS IN WITTEN’S SUPERSTRING FIELD THEORY

1989 ◽  
Vol 04 (21) ◽  
pp. 2063-2071
Author(s):  
GEORGE SIOPSIS
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
Invariant Theory ◽  
Higher Order ◽  
Contact Term ◽  
Tree Level ◽  
Gauge Invariant

It is shown that the contact term discovered by Wendt is sufficient to ensure finiteness of all tree-level scattering amplitudes in Witten’s field theory of open superstrings. Its inclusion in the action also leads to a gauge-invariant theory. Thus, no additional higher-order counterterms in the action are needed.

Enhanced Raman scattering by fractal clusters: Scale-invariant theory

1992 ◽  
Vol 46 (5) ◽  
pp. 2821-2830 ◽  
Author(s):  
Mark I. Stockman ◽  
Vladimir M. Shalaev ◽  
Martin Moskovits ◽  
Robert Botet ◽  
Thomas F. George
Keyword(s):  
Raman Scattering ◽  
Invariant Theory ◽  
Scale Invariant ◽  
Fractal Clusters ◽  
Enhanced Raman Scattering

scholarly journals Solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory

2008 ◽  
Vol 77 (3) ◽  
Author(s):  
Robert Foot ◽  
Archil Kobakhidze ◽  
Kristian L. McDonald ◽  
Raymond R. Volkas
Keyword(s):  
Invariant Theory ◽  
Hierarchy Problem ◽  
Scale Invariant ◽  
Hidden Sector
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