scholarly journals Arithmetic invariant theory

2014 ◽  
pp. 33-54 ◽  
Author(s):  
Manjul Bhargava ◽  
Benedict H. Gross
Keyword(s):  
Invariant Theory

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.

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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