scholarly journals On the conformal symmetry of exceptional scalar theories

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Kara Farnsworth ◽  
Kurt Hinterbichler ◽  
Ondřej Hulík
Keyword(s):  
Linear Algebra ◽  
Conformal Symmetry ◽  
Conformal Transformations ◽  
Spacetime Dimension ◽  
Real Form ◽  
Special Linear ◽  
Higher Dimensional ◽  
Lagrangian Form ◽  
Scalar Theories ◽  
Conformal Symmetries

Abstract The DBI and special galileon theories exhibit a conformal symmetry at unphysical values of the spacetime dimension. We find the Lagrangian form of this symmetry. The special conformal transformations are non-linearly realized on the fields, even though conformal symmetry is unbroken. Commuting the conformal transformations with the extended shift symmetries, we find new symmetries, which when taken together with the conformal and shift symmetries close into a larger algebra. For DBI this larger algebra is the conformal algebra of the higher dimensional bulk in the brane embedding view of DBI. For the special galileon it is a real form of the special linear algebra. We also find the Weyl transformations corresponding to the conformal symmetries, as well as the necessary improvement terms to make the theories Weyl invariant, to second order in the coupling in the DBI case and to lowest order in the coupling in the special galileon case.

(ANTI)COMMUTATIVITY OF THE HARMONIC CREATION AND ANNIHILATION OPERATORS

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1808-1818
Author(s):  
S. KUWATA ◽  
A. MARUMOTO
Keyword(s):  
Irreducible Representation ◽  
Harmonic Oscillator ◽  
Linear Algebra ◽  
Commutation Relation ◽  
Complex Number ◽  
Single Mode ◽  
Equation Of Motion ◽  
Sufficient Condition ◽  
Special Linear ◽  
Creation And Annihilation Operators

It is known that para-particles, together with fermions and bosons, of a single mode can be described as an irreducible representation of the Lie (super) algebra 𝔰𝔩2(ℂ) (2-dimensional special linear algebra over the complex number ℂ), that is, they satisfy the equation of motion of a harmonic oscillator. Under the equation of motion of a harmonic oscillator, we obtain the set of the commutation relations which is isomorphic to the irreducible representation, to find that the equation of motion, conversely, can be derived from the commutation relation only for the case of either fermion or boson. If Nature admits of the existence of such a sufficient condition for the equation of motion of a harmonic oscillator, no para-particle can be allowed.

scholarly journals O Ensino de Álgebra Linear para Engenharias utilizando o Scilab: aspectos matemáticos e computacionais / Teaching of Linear Algebra to Engineering Students using Scilab: mathematical and computational aspects

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Marcos Rodrigues Pinto
Keyword(s):  
Equilibrium Point ◽  
Linear Algebra ◽  
Learning Process ◽  
Engineering Students ◽  
Algebraic Thinking ◽  
The Other ◽  
Personal Computers ◽  
Special Linear ◽  
Computational Aspects ◽  
Teaching Learning

ABSTRACTThe teaching of Algebra, in special Linear Algebra, to engineering students, come changing its focus since the popularization of personal computers. Various specialized softwares has been developed and has become feasible to pay more attention in the algebraic thinking to solve problems and minus attention in the calculus itself. But one needs to be careful to not go to the extreme of this teaching-learning process. The teaching of Algebra using computational software must not mean the teaching of a sequence of commands and its syntaxes. On the other hand, it must not mean to memorize a sequence of definitions and theorems. So we propose a equilibrium point based on our experience with students of engineering that attended in our lessons of Algebra with Scilab software.RESUMOO ensino de álgebra, especialmente álgebra linear (AL), para estudantes de engenharia, vem mudando seu foco desde a populariozação dos computadores pessoais. Diversos softwares especializados têm sido desenvolvidos e tornado possível prestar mais atenção ao pensamento algébrico para a solução de problemas do que ao cálculo em si. Mas é necessário ter-se cuidado para não ocupar os extremos nesse processo de ensino-aprendizagem. O ensino de álgebra usando softwares não deve significar ensinar uma sequência de comandos e suas sintaxes. Também não deve significar memorizar uma sequência de definições e teoremas. Assim, propõe-se um ponto de equilíbrio baseado na experiência com estudantes de engenharia que participaram das aulas de AL utilizando o Scilab.

scholarly journals HAWKING RADIATION, GRAVITATIONAL ANOMALY, AND CONFORMAL SYMMETRY — THE ORIGIN OF UNIVERSALITY

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2082-2090 ◽  
Author(s):  
SATOSHI ISO
Keyword(s):  
Black Hole ◽  
Hawking Radiation ◽  
Conformal Transformation ◽  
Conformal Symmetry ◽  
Black Hole Horizon ◽  
Gravitational Anomaly ◽  
Universal Behavior ◽  
Higher Spin ◽  
Matter Fields ◽  
Conformal Symmetries

The universal behavior of Hawking radiation is originated in the conformal symmetries of matter fields near the black hole horizon. We explain the origin of this universality based on (1) the gravitational anomaly and its higher-spin generalizations and (2) conformal transformation properties of fluxes.

scholarly journals PEBBLE GAMES AND LINEAR EQUATIONS

2015 ◽  
Vol 80 (3) ◽  
pp. 797-844 ◽  
Author(s):  
MARTIN GROHE ◽  
MARTIN OTTO
Keyword(s):  
Linear Algebra ◽  
Linear Equations ◽  
Graph Isomorphism ◽  
Detailed Account ◽  
Base Level ◽  
Basic Colour ◽  
Higher Dimensional ◽  
Rational Arithmetic ◽  
Pebble Game ◽  
Fractional Isomorphism

AbstractWe give a new, simplified and detailed account of the correspondence between levels of the Sherali–Adams relaxation of graph isomorphism and levels of pebble-game equivalence with counting (higher-dimensional Weisfeiler–Lehman colour refinement). The correspondence between basic colour refinement and fractional isomorphism, due to Tinhofer [22; 23] and Ramana, Scheinerman and Ullman [17], is re-interpreted as the base level of Sherali–Adams and generalised to higher levels in this sense by Atserias and Maneva [1] and Malkin [14], who prove that the two resulting hierarchies interleave. In carrying this analysis further, we here give (a) a precise characterisation of the level k Sherali–Adams relaxation in terms of a modified counting pebble game; (b) a variant of the Sherali–Adams levels that precisely match the k-pebble counting game; (c) a proof that the interleaving between these two hierarchies is strict. We also investigate the variation based on boolean arithmetic instead of real/rational arithmetic and obtain analogous correspondences and separations for plain k-pebble equivalence (without counting). Our results are driven by considerably simplified accounts of the underlying combinatorics and linear algebra.

scholarly journals CORRESPONDENCE BETWEEN JORDAN–EINSTEIN FRAMES AND PALATINI-METRIC FORMALISMS

2010 ◽  
Vol 25 (39) ◽  
pp. 3279-3289 ◽  
Author(s):  
SALVATORE CAPOZZIELLO ◽  
FARHAD DARABI ◽  
DANIELE VERNIERI
Keyword(s):  
Cosmological Constant ◽  
Modified Gravity ◽  
Degrees Of Freedom ◽  
Conformal Symmetry ◽  
Conformal Transformations ◽  
Jordan And Einstein Frames

We discuss the conformal symmetry between Jordan and Einstein frames considering their relations with the metric and Palatini formalisms for modified gravity. Appropriate conformal transformations are taken into account leading to the evident connection between the gravitational actions in the two mentioned frames and the Hilbert–Einstein action with a cosmological constant. We show that the apparent differences between Palatini and metric formalisms strictly depend on the representation while the number of degrees of freedom is preserved. This means that the dynamical content of both formalism is identical.

scholarly journals AdS SEGMENT AND HIDDEN CONFORMAL SYMMETRY IN GENERAL NONEXTREMAL BLACK HOLES

2013 ◽  
Vol 22 (06) ◽  
pp. 1350029 ◽  
Author(s):  
HUIQUAN LI
Keyword(s):  
Black Holes ◽  
Conformal Symmetry ◽  
Rindler Space ◽  
Horizon Geometry ◽  
Conformal Symmetries

It is demonstrated that the near-horizon geometry of general nonextremal black holes can be described by a portion of AdS space. We show that the reason why hidden conformal symmetries near horizons of general nonextremal black holes are achieved in previous works is that the near-horizon geometries have been equivalently taken as these AdS segments rather than simply the Rindler space.

scholarly journals Reduced conformal symmetry

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Andreas Karch ◽  
Amir Raz
Keyword(s):  
Conformal Symmetry ◽  
Field Theories ◽  
Conformal Extension ◽  
Conformal Symmetries

Abstract We construct field theories in 2 + 1 dimensions with multiple conformal symmetries acting on only one of the spatial directions. These can be considered a conformal extension to “subsystem scale invariances”, borrowing the language often used for fractons.

scholarly journals The Combinatorics of Orbital Varieties Closures of Nilpotent Order 2 in sl${}_n$

10.37236/1918 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Anna Melnikov
Keyword(s):  
Symmetric Group ◽  
Linear Algebra ◽  
Young Tableau ◽  
Dominance Order ◽  
Young Tableaux ◽  
Young Diagrams ◽  
Special Linear ◽  
A Chain ◽  
Standard Young Tableaux ◽  
Right Order

We consider two partial orders on the set of standard Young tableaux. The first one is induced to this set from the weak right order on symmetric group by Robinson-Schensted algorithm. The second one is induced to it from the dominance order on Young diagrams by considering a Young tableau as a chain of Young diagrams. We prove that these two orders of completely different nature coincide on the subset of Young tableaux with 2 columns or with 2 rows. This fact has very interesting geometric implications for orbital varieties of nilpotent order 2 in special linear algebra $sl_n.$

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