Modern Physics Letters A

The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is addressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an illustration, one considers the anyon model restricted to the lowest Landau level of a strong magnetic field at low temperature, the generalization of this model to several particles species, and the one-dimensional Calogero model. One reviews a unified algorithm to compute the statistical mechanics of these systems. It is pointed out that Haldane's generalization of the Pauli's principle can be deduced from the anyon model in a strong magnetic field at low temperature.

When the (3+1) Einstein equations with matter are regarded as a subset of the (4+1) Kaluza–Klein equations in apparent vacuum, the recovery of appropriate properties of matter requires in general that the (4+1) metric depend on all the coordinates including the extra one. We display some consequences of (4+1) covariance through the use of exact solutions and coordinate transformations. We conclude that 4-D physics can be regarded as taking place on a hypersurface in 5-D, a mathematical condition which may be set by a physical one on the rest masses of particles.

The algebra of the integrated connections and of their traces is considered in the one-genus sector of classical and quantum Chern–Simons theory. In the classical case this algebra is braid-like and although the corresponding Jacobi identities are satisfied, the associated r-matrix does not satisfy the classical Yang–Baxter equations. However, it turns out this algebra originates a "quantum" algebra SU(2)_q given by its trace algebra. Canonical quantization of the above algebra is performed and a one-parameter expression for the operator ordering is considered. The same quantum algebra with a modified deformation parameter, nontrivially depending on ħ, is obtained.

A four-point dual amplitude, with nonlinear trajectories, is constructed from a two-parameter deformation of the harmonic oscillator algebra. The earlier versions of the q-deformed dual models are reproduced as limiting cases of the model introduced in the present work.

It is shown that the D-meson, whose light quark is the initial-pion valence quark and whose charmed quark is produced in annihilation of valence quarks and has got a large enough momentum, is really a leading meson in reactions like π⁻p → DX. If such annihilation of valence quarks from initial hadrons is impossible there must be no distinct leading effect.

The special role of the isoscalar mesons (σ and ω) in the NJL soliton is discussed. Stable soliton solutions are obtained when the most general ansatz compatible with vanishing grand spin is assumed. These solutions are compared to soliton solutions of a purely pseudoscalar Skyrme type model which is related to the NJL model by a gradient expansion and the limit of infinitely heavy (axial-) vector mesons.

The quantum BRST charge for the most general, two-dimensional, nonlinear, N = 4 quasi-superconformal algebra , whose linearization is the so-called 'large' N = 4 superconformal algebra, is constructed. The algebra has Kač–Moody component, and α = k⁻/k⁺. As a pre-requisite to our construction, we check the Jacobi identities and construct a classical BRST charge. Then, we analyze the quantum BRST charge nilpotency conditions and find the only solution, k⁺ = k⁻ = −2. The algebra is actually isomorphic to the SO(4)-based Bershadsky–Knizhnik nonlinear quasi-superconformal algebra. We argue about the existence of a new string theory with (i) the nonlinearly realized N = 4 worldsheet supersymmetry, (ii) non-unitary matter in a representation of k = −2 and c = −6, and (iii) negative 'critical dimension'.