Fibre bundle formulation of nonrelativistic quantum mechanics. IV. Mixed states and evolution transport's curvature

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum system is described by a state section (along paths) of a (Hilbert) fibre bundle. It's evolution is determined through the bundle (analogue of the) Schr\"odinger equation. Now the dynamical variables and the density operator are described via bundle morphisms (along paths). The mentioned quantities are connected by a number of relations derived in this work. The present fourth part of this series is devoted mainly to the fibre bundle description of mixed quantum states. We show that to the conventional density operator there corresponds a unique density morphism (along paths) for which the corresponding equations of motion are derived. It is also investigated the bundle description of mixed quantum states in the different pictures of motion. We calculate the curvature of the evolution transport and prove that it is curvature free iff the values of the Hamiltonian operator at different moments commute.Comment: 14 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. Minor style changes, a problem with the bibliography is corrected. Continuation of quant-ph/9803083, quant-ph/9803084, quant-ph/9804062 and quant-ph/9806046. For continuation of the series and related papers, view http://www.inrne.bas.bg/mathmod/bozhome

Fibre bundle formulation of nonrelativistic quantum mechanics. 0. Preliminary considerations: Quantum mechanics from a geometric-observer's viewpoint

We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is governed via (a kind of) a parallel transport in this bundle. Some problems concerning observables are considered. There are derived the equations of motion for the state sections and observables. We show that up to a constant the matrix of the coefficients of the evolution operator (transport) coincides with the matrix of the Hamiltonian of the investigated quantum system.Comment: 15 standard LaTeX 2e (11pt, A4) pages. The packages AMS-LaTeX and amsfonts are require

Variational separable expansion scheme for two-body Coulomb-scattering problems

We present a separable expansion approximation method for Coulomb-like potentials which is based on Schwinger variational principle and uses Coulomb-Sturmian functions as basis states. The new scheme provides faster convergence with respect to our formerly used non-variational approach.Comment: some typos correcte

Quenching of high-pT hadrons: Energy Loss vs Color Transparency

High-pT hadrons produced in hard collisions and detected inclusively bear peculiar features: (i) they originate from jets whose initial virtuality and energy are of the same order; (ii) such jets are rare and have a very biased energy sharing among the particles, namely, the detected hadron carries the main fraction of the jet energy. The former feature leads to an extremely intensive gluon radiation and energy dissipation at the early stage of hadronization, either in vacuum or in a medium. As a result, a leading hadron must be produced on a short length scale. Evaluation within a model of perturbative fragmentation confirms the shortness of the production length. This result is at variance with the unjustified assumption of long production length, made within the popular energy loss scenario. Thus we conclude that the main reason of suppression of high-pT hadrons in heavy ion collisions is the controlled by color transparency attenuation of a high-pT dipole propagating through the hot medium. Adjusting a single parameter, the transport coefficient, we describe quite well the data from LHC and RHIC for the suppression factor R_{AA} as function of pT, collision energy and centrality. We observe that the complementary effect of initial state interaction causes a flattening and even fall of R_{AA} at large pT. The azimuthal anisotropy of hadron production, calculated with no further adjustment, also agrees well with data at different energies and centralities.Comment: 17 pages, 19 figure

Quantum-mechanical description of in-medium fragmentation

We present a quantum-mechanical description of quark-hadron fragmentation in a nuclear environment. It employs the path-integral formulation of quantum mechanics, which takes care of all phases and interferences, and which contains all relevant time scales, like production, coherence, formation, etc. The cross section includes the probability of pre-hadron (colorless dipole) production both inside and outside the medium. Moreover, it also includes inside-outside production, which is a typical quantum-mechanical interference effect (like twin-slit electron propagation). We observe a substantial suppression caused by the medium, even if the pre-hadron is produced outside the medium and no energy loss is involved. This important source of suppression is missed in the usual energy-loss scenario interpreting the effect of jet quenching observed in heavy ion collisions. This may be one of the reasons of a too large gluon density, reported by such analyzes.Comment: 20 pages, 7 figure

Fibre bundle formulation of nonrelativistic quantum mechanics. III. Pictures and integrals of motion

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum system is described by a state section (along paths) of a (Hilbert) fibre bundle. It's evolution is determined through the bundle (analogue of the) Schr\"odinger equation. Now the dynamical variables and the density operator are described via bundle morphisms (along paths). The mentioned quantities are connected by a number of relations derived in this work. In this third part of our series we investigate the bundle analogues of the conventional pictures of motion. In particular, there are found the state sections and bundle morphisms corresponding to state vectors and observables respectively. The equations of motion for these quantities are derived too. Using the results obtained, we consider from the bundle view-point problems concerning the integrals of motion. An invariant (bundle) necessary and sufficient conditions for a dynamical variable to be an integral of motion are found.Comment: 19 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. New references and comments are added. Minor style chages. Continuation of quant-ph/9803083, quant-ph/9803084 and quant-ph/9804062. For continuation of the series view http://www.inrne.bas.bg/mathmod/bozhome

Comments on: "Quantum mechanics as a gauge theory of metaplectic spinor fields" by M. Reuter [Int.J.Mod.Phys. A13 (1998), 3835-3884; hep-th/9804036]

We point out how some mathematically incorrect passages in the paper of M. Reuter can be formulated in a rigorous way. The fibre bundle approach to quantum mechanics developed in quant-ph/9803083, quant-ph/9803084, quant-ph/9804062, quant-ph/9806046, quant-ph/9901039, and quant-ph/9902068 is compared with the one contained in loc. cit.Comment: 11 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. For related papers, view http://www.inrne.bas.bg/mathmod/bozhome

Heavy quarkonium production: Nontrivial transition from pA to AA collisions

Two novel QCD effects, double color filtering and mutual boosting of the saturation scales in colliding nuclei, affect the transparency of the nuclei for quark dipoles in comparison with proton-nucleus collisions. The former effect increases the survival probability of the dipoles, since color filtering in one nucleus makes the other one more transparent. The second effect acts in the opposite direction and is stronger, it makes the colliding nuclei more opaque than in the case of pA collisions. As a result of parton saturation in nuclei the effective scale is shifted upwards, what leads to an increase of the gluon density at small x. This in turn leads to a stronger transverse momentum broadening in AA compared with pA collisions, i.e. to an additional growth of the saturation momentum. Such a mutual boosting leads to a system of reciprocity equations, which result in a saturation scale, a few times higher in AA than in pA collisions at the energies of LHC. Since the dipole cross section is proportional to the saturation momentum squared, the nuclei become much more opaque for dipoles in AA than in pA collisions. For the same reason gluon shadowing turns out to be boosted to a larger magnitude compared with the product of the gluon shadowing factors in each of the colliding nuclei. All these effects make it more difficult to establish a baseline for anomalous J/Psi suppression in heavy ion collisions at high energies.Comment: 10 pages 8 figures. The accuracy of calculations is improve