27 research outputs found
Non-abelian Harmonic Oscillators and Chiral Theories
We show that a large class of physical theories which has been under
intensive investigation recently, share the same geometric features in their
Hamiltonian formulation. These dynamical systems range from harmonic
oscillations to WZW-like models and to the KdV dynamics on . To the
same class belong also the Hamiltonian systems on groups of maps.
The common feature of these models are the 'chiral' equations of motion
allowing for so-called chiral decomposition of the phase space.Comment: 1
Glimpses of the Octonions and Quaternions History and Todays Applications in Quantum Physics
Before we dive into the accessibility stream of nowadays indicatory
applications of octonions to computer and other sciences and to quantum physics
let us focus for a while on the crucially relevant events for todays revival on
interest to nonassociativity. Our reflections keep wandering back to the
two square identity and then via the four
square identity up to the eight square identity.
These glimpses of history incline and invite us to retell the story on how
about one month after quaternions have been carved on the bridge
octonions were discovered by , jurist and
mathematician, a friend of . As for today we just
mention en passant quaternionic and octonionic quantum mechanics,
generalization of equations for octonions and triality
principle and group in spinor language in a descriptive way in order not
to daunt non specialists. Relation to finite geometries is recalled and the
links to the 7stones of seven sphere, seven imaginary octonions units in out of
the cave reality applications are appointed . This way we are welcomed
back to primary ideas of , and other distinguished
fathers of quantum mechanics and quantum gravity foundations.Comment: 26 pages, 7 figure
Quaternionic and Octonionic Spinors. A Classification
Quaternionic and octonionic realizations of Clifford algebras and spinors are
classified and explicitly constructed in terms of recursive formulas. The most
general free dynamics in arbitrary signature space-times for both quaternionic
and octonionic spinors is presented. In the octonionic case we further provide
a systematic list of results and tables expressing, e.g., the relations of the
octonionic Clifford algebras with the cosets over the Lorentz algebras,
the identities satisfied by the higher-rank antisymmetric octonionic tensors
and so on. Applications of these results range from the classification of
octonionic generalized supersymmetries, the construction of octonionic
superstrings, as well as the investigations concerning the recently discovered
octonionic -superalgebra and its superconformal extension.Comment: 24 pages, LaTe
Harmonic BRST Quantization of Systems with Irreducible Holomorphic Boson and Fermion Constraints
We show that the harmonic Becchi-Rouet-Stora-Tyutin method of quantizing
bosonic systems with second-class constraints or first-class holomorphic
constraints extends to systems having both bosonic and fermionic second-class
or first-class holomorphic constraints. Using a limit argument, we show that
the harmonic BRST modified path integral reproduces the correct Senjanovic
measure.Comment: 11 pages, phyzz
NONLINEAR SYSTEM IDENTIFICATION VIA WAVELET EXPANSIONS
Abstract: The paper deals with the problem of recovering a nonlinearity in a class of nonlinear dynamical systems of block-oriented structure.The class includes a large number of previously examined block-oriented models.The sought nonlinearity is allowed to have singular points like discontinuities and points of non-differentiability. In order to cope with such general nonlinearities the theory of wavelet expansions is applied. A major advantage of these expansions is adaptation to erratic behavior of the nonlinearity and local adaptation to the degree of smoothness of an unknown characteristic. Hence a wavelet-based identification algorithm of the nonlinearity is proposed and conditions for the convergence of the algorithm are given. For nonlinearities satisfying some smoothing conditions the rate of convergence is also evaluated