scholarly journals Lie algebra in quantum physics by means of computer algebra

2017 ◽  
Author(s):  
Ichio Kikuchi ◽  
Akihito Kikuchi
Keyword(s):  
Quantum Mechanics ◽  
Angular Momentum ◽  
Lie Algebra ◽  
Computer Algebra ◽  
Quantum Physics ◽  
Character Formula ◽  
Weyl Character Formula ◽  
Weight Modules

This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold-way model, and the usage of Weyl character formula (in order to construct weight modules, and to count correctly the degeneracy

Quantum mechanics and the geometry of the Weyl character formula

1990 ◽  
Vol 337 (2) ◽  
pp. 467-486 ◽  
Author(s):  
Orlando Alvarez ◽  
I.M. Singer ◽  
Paul Windey
Keyword(s):  
Quantum Mechanics ◽  
Character Formula ◽  
Weyl Character Formula

LOCAL ANALYSIS BY WAVELETS VERSUS NONLOCAL FOURIER ANALYSIS

2007 ◽  
Vol 05 (01n02) ◽  
pp. 89-95
Author(s):  
J. R. CROCA
Keyword(s):  
Quantum Mechanics ◽  
Fourier Analysis ◽  
Quantum Physics ◽  
Plane Waves ◽  
Local Analysis ◽  
Mathematical Tool ◽  
Space Harmonic ◽  
New Approach ◽  
Spatial Frequencies ◽  
Temporal And Spatial

Orthodox quantum mechanics has another implicit postulate stating that temporal and spatial frequencies of the Planck–Einstein and de Broglie formulas can only be linked with the infinite, in time and space, harmonic plane waves of Fourier analysis. From this assumption, nonlocality either in space and time follows directly. This is what is called Fourier Ontology. In order to build nonlinear causal and local quantum physics, it is necessary to reject Fourier ontology and accept that in certain cases a finite wave may have a well defined frequency. Now the mathematical tool to describe this new approach is wavelet local analysis. This more general nonlinear local and causal quantum physics, in the limit of the linear approximation, contains formally orthodox quantum mechanics as a particular case.

scholarly journals The elliptic Weyl character formula

2014 ◽  
Vol 150 (7) ◽  
pp. 1196-1234 ◽  
Author(s):  
Nora Ganter
Keyword(s):  
Line Bundle ◽  
Lie Groups ◽  
Theoretical Framework ◽  
Flag Variety ◽  
Schubert Calculus ◽  
Character Formula ◽  
Elliptic Cohomology ◽  
Image Position ◽  
Weyl Character Formula

AbstractWe calculate equivariant elliptic cohomology of the partial flag variety$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G/H$, where$H\subseteq G$are compact connected Lie groups of equal rank. We identify the${\rm RO}(G)$-graded coefficients${\mathcal{E}} ll_G^*$as powers of Looijenga’s line bundle and prove that transfer along the map$$\begin{equation*} \pi \,{:}\,G/H\longrightarrow {\rm pt} \end{equation*}$$is calculated by the Weyl–Kac character formula. Treating ordinary cohomology,$K$-theory and elliptic cohomology in parallel, this paper organizes the theoretical framework for the elliptic Schubert calculus of [N. Ganter and A. Ram,Elliptic Schubert calculus, in preparation].

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