Modern Physics Letters A

The degeneracy structure of the eigenspace of the N-particle Calogero–Sutherland model is studied from an algebraic point of view. Suitable operators satisfying SU(2) algebras and acting on the degenerate eigenspace are explicitly constructed for the two-particle case and then appropriately generalized to the N-particle model. The raising and lowering operators of these algebras connect the states, in a subset of the degenerate eigenspace, with each other.

We attempt to treat the very early Universe according to quantum mechanics. Identifying the scale factor of the Universe with the width of the wave packet associated with it, we show that there cannot be an initial singularity and that the Universe expands. Invoking the correspondence principle, we obtain the scale factor of the Universe and demonstrate that the causality problem of the standard model is solved.

Using the "star" construction for the Kashiwara–Miwa model we obtain the set of elliptic solvable IRF models. Part of these models turns out to be some particular case of the cyclic solid-on-solid (CSOS) models.

The q-symmetric state is constructed by using su_q(n)-covariant multimode oscillator and its mode operators are expressed in terms of the q-symmetric states and the q=0 quon oscillators.

The combined effect of the magnetic field background in the form of a singular vortex and the Dirichlet boundary condition at the location of the vortex on the vacuum of quantized scalar field is studied. We find the induced vacuum energy density and current to be periodic functions of the vortex flux and holomorphic functions of the space dimension.

We present an N=1 supersymmetric extension of a spin-charge separated effective SU(2)×U_S(1) "particle-hole" gauge theory of excitations about the nodes of the gap of a d-wave planar magnetic superconductor. The supersymmetry is achieved without introducing extra degrees of freedom, as compared to the nonsupersymmetric models. The only exception, the introduction of gaugino fields, finds a natural physical interpretation as describing interlayer coupling in the statistical model. The low-energy continuum theory is described by a relativistic (2+1)-dimensional supersymmetric CP¹ σ-model with Gross–Neveu–Thirring-type four-fermion interactions. We emphasize the crucial role of the CP¹ constraint by inducing a nontrivial dynamical mass generation for fermions (and thus superconductivity), in a way compatible with manifest N=1 supersymmetry. We also give a preliminary discussion of nonperturbative effects. We argue that supersymmetry suppresses the danger of superconductivity instanton contributions to the mass of the perturbatively massless gauge boson of the unbroken U(1) subgroup of SU(2). Finally, we point out the possibility of applying these ideas to effective gauge models of spin-charge separation in one-space dimensional superconducting chains of holons, which, for example, have recently been claimed to be important in the stripe phase of underdoped cuprates.

An idea of possible anomalous contribution of nonperturbative origin to the nucleon spin was examined by analyzing data on spin asymmetries in polarized deep inelastic scattering of leptons on nucleons. The region of high Bjorken x was explored. It was shown that experimental data available at present do not exhibit any evidence for this effect.

We construct a two-parameter covariant differential calculus on the quantum h-exterior plane. We also give a deformation of the two-dimensional fermionic phase space.