We propose a group-theoretical approach to the generalized oscillator algebra Aκ recently investigated in J. Phys. A: Math. Theor. 2010, 43, 115303. The case κ ≥ 0 corresponds to the noncompact group SU(1,1) (as for the harmonic oscillator and the Pöschl-Teller systems) while the case κ < 0 is described by the compact group SU(2) (as for the Morse system). We construct the phase operators and t...

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for SU(2), SO(...

1. The unit sphere in R and the classification of regular solids 1 2. Symmetries of platonic solids 3 3. Basic representation theory of finite groups 6 4. Haar basis of L(R) 17 5. Haar multiresolution of L(R) 20 6. Daubechies wavelets 22 7. Wavelets and group representations 24 8. Numerical integration on the sphere 25 9. Unique factorization domains and Hilbert’s Nulstellensatz 27 10. Spherica...

String models are designed to provide a covariant description of internal space-time structure of relativistic particles. The string is a limiting case of a series of massive beads like a pearl necklace. In the limit of infinite-number of zero-mass beads, it becomes a field-theoretic string. Another interesting limit is to keep only two pearls by eliminating all others, resulting in a harmonic ...

The process some call ‘categorification’ consists of interpreting set-theoretic structures in mathematics as derived from category-theoretic structures. Examples include the interpretation of as the Burnside rig of the category of finite sets with product and coproduct, and of [x] in terms the category of combinatorial species. This has interesting applications to quantum mechanics, and in part...

This paper aims at proposing a measure of speech rhythm based on the inference of the coupling strength between the syllable oscillator and the stress group oscillator of an underlying coupled oscillators model. This coupling is inferred from the linear regression between the stress group duration and the number of syllables within the group, as well as from the multiple linear regression betwe...

Abstract We study the Li–Yau inequality for heat equation corresponding to Dunkl harmonic oscillator, which is a nonlocal Schrödinger operator parameterized by reflections and multiplicity functions. In particular case when reflection group isomorphic ℤ 2 d {\mathbb{Z}...