Han-Ying Guo

The q-deformed oscillator model and the vibrational spectra of diatomic molecules☆

Abstract A model of a q -oscillator with quantum group symmetry H q (4) is put forward. The representations of the q -oscillator algebra H q (4) and solutions to the quantum q -oscillator system are provided. We find that the energy spectrum of the q -oscillator bears the essential properties of the observed spectra of diatomic molecules. When the parameters are determined phenomenologically, the spectrum of the q -oscillator coincides with the infrared, vibrational Raman spectra and vibrational structure of electronic transitions of the diatomic molecule.

Higgs as gauge fields on discrete groups and Standard Models for electroweak and electroweak-strong interactions

We complete the construction of the gauge theory on discrete groups coupled to fermions in the spirit of non-commutative geometry. We show that a simple Higgs field is such a gauge field with respect toZ2-gauge symmetry overM4 and the Yukawa coupling between Higgs and fermions is automatically introduced via minimum coupling principle. TheZ2-symmetry is taken to be Θ={e, r=(CPT)2}, a sub-symmetry of the CPT transformations. The Weinberg-Salam model for the electroweak interaction as well as the Standard Model for the electroweak-strong interaction are reformulated in detail.

SUq,h(cross) to 0(2) and SUq,h(cross)(2), the classical and quantum q-deformations of the SU(2) algebra. II. The Hopf algebra, the Yang-Baxter equation and multi-deformed algebraic structures

For pt. I see ibid., vol.23, p.4185 (1990). The SUq(2) algebra is realized by means of both the Poisson brackets in classical mechanics and commutators in quantum mechanics in a system with q-deformed oscillators of two different types. The structures of the Hopf algebra and the quantum Yang-Baxter equation are also discussed on a quantum level. A set of j-representations of the quantum algebra SUq(2) is constructed based on the type-II q-oscillators. Multi-deformations of the oscillators of the two types and multi-deformed algebras expressed in Poisson brackets as well as in Lie brackets are proposed.

Non-Bosonic Excitations in q-Oscillator System for q a Root of Unity*

The systems of q-deformed oscillators of type two are studied in the case of q being the roots of unity. Non-bosonic excitations are found in (quantum mechanical) q-oscillators, and the classical mechanical counterparts and the saturation property are given. Especially when rank k is near 4, the excitations are found violating the Pauli exclusion principle, and possible physical interpretation is investigated.

SUq,h(cross) to 0(2) and SUq,h(cross)(2), the classical and quantum q-deformations of the SU(2) algebra. III. When q is a root of unity

For pt.II see ibid., vol.23, p.5371 (1990). The q-oscillator of type one and the classical and the quantum q-deformations of SU(2) algebra realized through the q-oscillators are studied in the case of q being roots of unity, i.e. qk=1. The q-excitations are found to be non-bosonic. In particular, when k is of rank 4 and 6, the q-excitations are shown to be fermionic and parafermionic respectively.

The Algebras of Meromorphic Vector Fields and the Bases of Meromorphic λ-Differentials on Riemann Surfaces*

The algebras of meromorphic vector fields and the bases of meromorphic λ-differentials with multipoles are constructed explicitly on general genus Riemann surfaces. For Riemann sphere the central extension of the algebra is also given.

CECH-DE RHAM COMPLEX AS GAUGE GROUP COHOMOLOGY

We show that the Cech-de Rham complexes can be constructed by means of the generalized secondary classes and their definitely combinatory forms, then in this sense these complexes turn out to be the gauge group cohomologies.

HAMILTONIAN OF LOW-ENERGY PROCESSES FOR CUPRATE OXIDE SUPERCONDUCTORS

Abstract An extended one-band Hubbard model for low energy processes in cuprate oxide superconductors is proposed. The Hamiltonian includes the interaction between two electrons on different sites of the nearest neighbors to emphasize the role played by the Cuue5f8O mixing. The difference from other Hubbard-like models is discussed. An MMP-like antiferromagnetic spin fluctuation toy model is obtained under a weak Cuue5f8O mixing restriction.

Electron-phonon interaction of the C60 intra-molecule mode in A3C60

Abstract The electron-phonon interaction induced by the intra-molecule mode of C 60 is computed by paying attention to the interference among the C atoms in a cell. The result supports the opinion that is the electron-phonon interaction induced by the low frequency inter-molecule mode that resulted in the superconductivity of A 3 C 60 .

Beltrami Algebra and Its Operator Formalism

We construct the Beltrami algebra related to quasiconformal transformation on torus and its BRST formalism. The formalism shows the central charge of the Beltrami algebra is equal to 28, that is .