On the statistics of quantised dissipative systems

Magnetic circular dichroism (MCD) of theA- andB-absorption band region has been obtained at 4.2 K and 50 kG in KI:Ga⁺, KI:In⁺, and KI:Sn²⁺. The MCD spectra indicate the complex nature of these bands more clearly than the absorption spectra themselves do. TheA-band MCD consists in all cases of a positive and a negative part reflecting the structure of the absorption band. TheB-band MCD shows three peaks, two positive peaks at 4.34 and 4.41₅ eV (4.09 and 4.17₅ eV) and a negative peak at 4.38 eV (4.12₅ eV) in KI:Ga⁺ (KI:In⁺). TheB-band in KI:Sn²⁺ consists of a shoulder (b ₀) at 3.76 eV and a main band which has at least 5 sub-peaks (b ₁~b ₅) at 3.82₁, 3.84₁, 3.86₁, 3.88₀, and 3.89₅ eV; each of the subpeaks (b ₁~b ₅) gives a derivative-like MCD.The MCD shape functionf() for the transitiona _1g ² a _1g t _1u has been obtained for one set of parameter values by using the classical Franck-Condon approximation and the Monte Carlo integration method. The result can explain the observed salient features of theB- as well asA-band MCD's, indicating the validity of the Franck-Condon approximation and the interaction mode coordinates.     

On the Dirichlet problem of chromodynamics

We show that the solutions to the euclidean field equations of chromodynamics are not in general uniquely determined by their boundary values. In the two-dimensional case there is a denumerable infinity of solutions satisfying any prescribed set of Dirichlet boundary data.     

On inertial frames in the theory of quantised fields

The physical significance of time symmetry and the difficulty of the definition of an inertia frame (reference frame) is considered for a quantum field of material points with special consideration of the electrodynamics of a superconducting body.     

On the vacuum rearrangement in massless chromodynamics

It is shown that in the weak coupling limit the Bethe-Salpeter equation of massless chromodynamics admits a colourless tachyon solution when the number of quark multiplets n ? n_c, where for the colour group SU(N) the critical value n_c ≈ 0.14 N³/(N² ? 1). When n ? n_c, the vacuum rearrangement results in the gluons acquiring a mass; n > n_c all particles remain massless.     

On de-globalization in quantum chromodynamics

The recent discovery and resummation of a class of single logarithmic effects (non-global logs), has a significant impact on several QCD observables ranging from the classic Sterman-Weinberg jet definition to currently studied event shapes and rapidity gap observables. The discovery of the above effects overturns, for example, the common wisdom that hadronic energy flow in limited inter-jet regions is dictatedprimarily by the colour flow of the underlying hard partonic subprocess. We discuss some features of non-global logs and the rapid progress being made in estimating and controlling such corrections.     

The static metrics with cylindrical symmetry describing a model of cosmic strings

We discuss a set of static metrics with cylindrical symmetry describing the interior and exterior space-time of a model of cosmic strings considered recently in cosmology. The interior metric depends on one arbitrary function and the exterior on one constant. We find the relation between this constant and the linear mass density of the cosmic string. A cosmic string can be also treated as a line source in the framework of the distribution-valued curvature formalism which allows us to obtain again the same relation.     

A description of the quantised nonlinearinterferometer

A formalism is presented which describes in an elegant way the general output field of the nonlinear interferometer as two-mode entangled coherent states. We also show that entangled coherent states can also be produced for product coherent states without the need for the interferometric configuration.     

On the light meson mass formulae from quantum chromodynamics

We reconsider the Gell-Mann-Okubo light meson mass formulae using the moment sum rules ratios and taking into account non-leading quark masses and vacuum condensate effects. We also extract the strange quark mass value from the ?-ρ mass difference. The poorly known masses of the (I=0,J ^PC =0⁺⁺) scalar mesons are discussed.     

关于转动弦的波动方程

数学物理方法的一些学习指导书或教科书上给出了两种转动弦的波动方程,但没有考虑Coriolis力的影响,其讨论方法存在不正确(竖直转动重弦)或不全面(水平转动轻弦)之处.重新讨论了两种转动弦的波动方程及其求解问题.     

On the stability of AdS black strings

We explore via linearized perturbation theory the Gregory–Laflamme instability of the black string solutions of Einstein's equations with negative cosmological constant recently discussed in literature. Our results indicate that the black strings whose conformal infinity is the product of time and Sd−3×S¹$S^{d-3}\times S^1$ are stable for large enough values of the event horizon radius. All topological black strings are also classically stable. We argue that this provides an explicit realization of the Gubser–Mitra conjecture.     

On the quark mass dependence of the parameters of quantum chromodynamics

The running coupling constant and quark masses in QCD are calculated in the one-loop approximation using the 3-gluon vertex to define the coupling constant. Our results differ for finite quark masses from those reported previously in the literature. We discuss the origin of this apparent discrepancy. We also make some comments on the gauge dependence of the QCD parameters.     

On gauge invariant bosonic strings

Following Witten, an associative product is constructed for fields on open strings, with BRST ghosts, which has the same topological structure as that in the light-cone gauge. The product is shown to be well defined on a certain class of string functionals. The corresponding action is that of Chern-Simons. The relation of this product to that of others is discussed.     

On the unitarity of gauged non-compact WZNW strings

In this paper we investigate the unitarity of gauged non-compact WZNW strings, i.e., string theories formulated as G/H^′$G/H^{\prime }$ WZNW models, where G   is a non-compact group. These models represent string theories on non-trivial curved space–times with one time-like component. We will prove that for the class of models connected to Hermitian symmetric spaces, and a natural set of discrete highest weight representations, the BRST formulation, in which the gauging is defined through a BRST condition, yields unitarity. Unitarity requires the level times the Dynkin index to be an integer, as well as integer valued highest weights w.r.t. the compact subalgebra. We will also show that the BRST formulation is not equivalent to the conventional GKO coset formulation, defined by imposing a highest weight condition w.r.t. H^′$H^{\prime }$. The latter leads to non-unitary physical string states. This is, to our knowledge, the first example of a fundamental difference between the two formulations.     

On the harmonic gauge in the quantization of strings

We discuss the path integral quantization of the bosonic string in the (non-background covariant) harmonic gauge, confronting it with the recently proposed background covariant version. The critical dimension as well as the ghost number current anomaly is computed. Whereas the latter has been found to vanish in the background covariant harmonic gauge, we obtain the same result as in the conformal gauge. This apparent discrepancy is resolved by detecting a new anomaly pertaining to the background covariant version of the harmonic gauge.     

On vibrating strings and information theory

The problem addressed in concreto is the relation of information provided by vibrating strings to that provided by systems describable with equations of one degree of freedom. Whereas the mathematical physics of vibrating strings is based on the wave equation—a second-order differential equation of at least two degrees of freedom—a quantum model of information theory has only been considered for a mechanical system of one degree of freedom.     

On the conjectured transition of black holes into strings

It is argued that if black holes change into strings in the last stage of their evaporation, as has been conjectured, they will go into massless strings directly rather than via an intermediate state containing a massive string.     

On gauge invariance and perturbative calculations in quantum chromodynamics

It is possible to regularize infra-red divergences of QCD by giving a mass to the gluon in such a way that the Becchi-Rouet-Stora invariance of the action is preserved. This regularization allows straightforward extension of dispersive techniques to the computation of radiative corrections to on-shell processes in QCD. Problems of gauge dependence, however, exist: care must be taken in the choice of the expansion parameter and only physically meaningful processes are gauge independent, e.g., cross sections summed over all final degenerate states.