Fermions obstruct dimensional reduction in hot QCD

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information on potentials implemented in the form of stochastic processes. Its specific advantages are the possibilities to deal with heterogeneous data and to express a priori information explicitly in terms of the potential of interest. A numerical solution in maximum a posteriori approximation is obtained for one-dimensional problems. As nonparametric estimates, the results depend strongly on the implemented a priori information.     

Hot twists for the single-point model of large-N QCD

We construct two types of twists for the SU(N→∞) twisted-Eguchi-Kawai model, which mimic a periodic boundary condition in the temporal direction only and over an arbitrary extent N₀. In this way we introduce finite temperature (T=N₀^?1 in lattice units) in the single-point model. In weak coupling one gets the correct planar expansion.     

The pion form factor from lattice QCD with two dynamical flavours

We compute the electromagnetic form factor of the pion, using non-perturbatively O(a) improved Wilson fermions. The calculations are done for a wide range of pion masses and lattice spacings. We check for finite size effects by repeating some of the measurements on smaller lattices. The large number of lattice parameters we use allows us to extrapolate to the physical point. For the square of the charge radius we find fm², in good agreement with experiment. PACS 12.38.Gc; 13.40.Gp; 14.40.-n     

Additive quark model with six flavours

Under the assumption of theSU(6) internal hadron symmetry, a six quark model with different flavours is proposed. There are constructedSU(6) multiplets of mesonsJ ^p =0^}, 1^– and baryonsJ ^p =3/2⁺, 1/2⁺ according to the irreducible representations ofSU(6) group. It is natural to assume that this symmetry is broken by heaviness of quarks. That gave us the possibility to derive mass sum rules for these hadrons and make theoretical predictions of masses for bottom vector mesons.Dedicated to Academician Václav Votruba on the occasion of his seventieth birthday.The author is indebted to Dr. M. Bedná for helpful discussions.     

Chiral phase structure of QCD with many flavors

We investigate QCD with a large number of massless flavors with the aid of renormalization group flow equations. We determine the critical number of flavors separating the phases with and without chiral symmetry breaking in SU(N_c) gauge theory with many fermion flavors. Our analysis includes all possible fermionic interaction channels in the pointlike four-fermion limit. Constraints from gauge invariance are resolved explicitly and regulator-scheme dependencies are studied. Our findings confirm the existence of an N_f window where the system is asymptotically free in the ultraviolet, but remains massless and chirally invariant on all scales, approaching a conformal fixed point in the infrared. Our prediction for the critical number of flavors of the zero-temperature chiral phase transition in SU(3) is N_f^cr=10.0±0.29 (fermion)^+1.55_-0.63 (gluon), with the errors arising from approximations in the fermionic and gluonic sectors, respectively. PACS 11.10.Hi, 11.15.Tk, 11.30.Rd     

A unified model of weak,electromagnetic and strong interactions based on six flavours and “six” colours

A unified model of weak, electromagnetic and strong interactions based on the group SO₆ ? SO₆ ? SO₆ is proposed. The model is anomaly free. Other consequences are: the vector character of colour couplings, a weak mixing angle sin²θ_w = 0.239 and a unification mass 5 orders of magnitude lower than the one required by SU₅.     

Criticality of QCD in a holographic QCD model with critical end point

The thermodynamics of strongly interacting matter near the critical end point are investigated in a holographic QCD model, which can describe the QCD phase diagram in T-μ plane qualitatively. Critical exponents along different axes(α,β,γ,δ) are extracted numerically. It is given that α≈0,β≈0.54,γ≈1.04, and δ≈2.97,which is similar to the three-dimensional Ising mean-field approximation and previous holographic QCD model calculations. We also discuss the possibilities to go beyond the mean field approximation by including the full back-reaction of the chiral dynamics in the holographic framework.     

Some QCD estimates of the production of heavy quark flavours in hadron-hadron collisions

Quantum chromodynamic perturbation theory is used to investigate the hadronic production of heavy quark flavours. The theory is applied principally to the data on charmed meson production. Particular emphasis is placed on comparing data with this calculation in the specific region of phase space in which the data are taken. The general results of this approach are presented so that comparisons with data from future experiments on charm and heavier flavour production should be possible.     

Optical colours and polarization of a model reflection nebula

Simple models of a reflection nebula in the form of a plane-parallel slab containing smooth spherical solid particles in submicron size range have been considered. Single scattering has been assumed. The effect of varying the composition and size distribution function of the grains have been brought out in the calculations using Mie theory of scattering. The analytical part of the geometry of the problem has been treated quite rigorously and the resulting expression for nebular intensity has been presented in a somewhat new form. In this paper, the case of the star behind the nebula has been examined. A comparison of the theoretical results with the observations of the Merope nebula shows that the dirty ice grains with index of refraction about 1·3–0·1i and size parametera ₀ = 0·5μ give reasonable agreement with the colours. Simultaneously, the polarization in the visual and blue wavelength bands agree approximately up to offset angle of 6 minutes of arc. The larger offset angles pose an intriguing problem. The general trends of nebular colours and polarization with variation of real and imaginary parts of index of refraction and the size distribution parameter have been tabulated to serve as a guide for further study of reflection nebulae with the star in the rear. A part of this work was presented at the first scientific meeting of the Astronomical Society of India, held on 27 and 28 February 1974 at Hyderabad. An erratum to this article is available at .     

QCD and a holographic model of hadrons

We propose a five-dimensional framework for modeling low-energy properties of QCD. In the simplest three parameter model we compute masses, decay rates and couplings of the lightest mesons. The model fits experimental data to within 10%. The framework is a holographic version of the QCD sum rules, motivated by the anti-de Sitter/conformal field theory correspondence. The model naturally incorporates properties of QCD dictated by chiral symmetry, which we demonstrate by deriving the Gell-Mann-Oakes-Renner relationship for the pion mass.     

Fermions and associated bosons of one-dimensional model

The representation of the canonical commutation relations involved in the construction of boson operators from fermion operators according to the recipe of the neutrino theory of light is studied. Starting from a cyclic Fock-representation for the massless fermions the boson operators are reduced by the spectral projectors of two charge-operators and form an infinite direct sum of cyclic Fock-representations. Kronig's identity expressing the fermion kinetic energy in terms of the boson kinetic energy and the squares of the charge operators is verified as an identity for strictly selfadjoint operators. It provides the key to the solubility ofLuttinger's model. A simple sufficient condition is given for the unitary equivalence of the representations linked by the canonical transformation which diagonalizes the total Hamiltonian.Work supported by the National Science Foundation.     

Fermions in a Kerr-Newman space-time

The aim of this paper is to put the U(1) -gauge theory of fermions in the spacetime described by a Kerr-Newman metric. The field equations have rather complicated expressions essentially different from the Minkowskian spacetime.     

Effects of perturbative exchanges in a QCD string model

The QCD string model for baryons derived by Yu. A. Simonov and used for the calculation of baryon magnetic moments in a previous paper is extended to include also perturbative gluon and meson exchanges. The mass spectrum of the baryon multiplet is studied. For the meson interaction, either pseudoscalar or pseudovector coupling is used. Predictions are compared with the experimental data. Besides these exchanges, the influence of excited quark orbitals on the baryon ground state are considered by performing a multichannel calculation. The nucleon-Δ splitting increases due to the mixing of higher quark states, while the baryon magnetic momenta decrease. The multichannel calculation with perturbative exchanges is shown to yield reasonable magnetic moments, while the mass spectrum is close to experiment.     

Phase structure of a surface model with many fine holes

We study the phase structure of a surface model by using the canonical Monte Carlo simulation technique on triangulated, fixed connectivity, and spherical surfaces with many fine holes. The size of a hole is assumed to be of the order of lattice spacing (or bond length) and hence can be negligible compared to the surface size in the thermodynamic limit. We observe in the numerical data that the model undergoes a first-order collapsing transition between the smooth phase and the collapsed phase. Moreover the Hasudorff dimension H remains in the physical bound, i.e., H < 3 not only in the smooth phase but also in the collapsed phase at the transition point. The second observation is that the collapsing transition is accompanied by a continuous transition of surface fluctuations. This second result distinguishes the model in this paper and the previous one with many holes, whose size is of the order of the surface size, because the previous surface model with large-sized holes has only the collapsing transition and no transition of surface fluctuations.     

Properties of quark matter in a new quasiparticle model with QCD running coupling

The running of the QCD coupling in the effective mass causes thermodynamic inconsistency problem in the conventional quasiparticle model. We provide a novel treatment which removes the inconsistency by an effective bag constant. The chemical potential dependence of the renormalization subtraction point is constrained by the Cauchy condition in the chemical potential space. The stability and microscopic properties of strange quark matter are then studied within the completely self-consistent quasiparticle model, and the obtained equation of state of quark matter is applied to the investigation of strange stars. It is found that our improved model can describe well compact stars with mass about two times the solar mass, which indicates that such massive compact stars could be strange stars.     

QCD and the string model

Infinitisimal variations of the path-dependent phase factor P exp(i∫_σA_μdz_μ) in gauge theory are studied. They are shown to satisfy differential equations which are equivalent to those for a quantized string if the gauge fields meet certain constraints.     

Fermions and bosons in a two-dimensional world

We derive the formal equivalence of a free massless two-dimensional theory and a free massless two-dimensional boson theory constructed from the bilinear products of the self-same fermion theory. The sense of this equivalence is investigated. Using a box normalization, it is found that the fermion states are Glauber coherent states of bosons, where the boson vacuum is the ground state of the charge sector corresponding to the given fermion state. The massless boson is the Goldstone boson and the degenerate vacua are the ground states of the various charge sectors. A complete operator identity between fermion and boson operators can be obtained, but to do this an additional boson operator must be introduced which cannot be defined in terms of bilinear products of the fermion operators. Doing this makes the charge spectrum continuous.     

Fermions in interaction with time-dependent fields

We solve a two-dimensional model describing the interaction of fermions with time-dependent external fields. We work out the second quantized formulation and obtain conditions for equivalence of representations at different times. This implies the existence of sectors which describe charged states. We obtain the time dependence of charges and observe that charge differences become integer for unitary equivalent states. For scattering we require the equivalence of in- and out-representations; nevertheless charged sectors may be reached by suitable interactions and ionization is possible.