The jet quenching in high energy nuclear collisions and quark-gluon plasma

e investigate the energy loss of quark and gluon jets in quark-gluon plasma produced in central Au+Au collisions at RHIC energy. We use the physical characteristic of initial and mixed phases, which were found in effective quasiparticle model for SPS and RHIC energy. At investigation of energy loss we take into account also the production of hot glue at first stage. The energy loss in expanding plasma is calculated in dominant first order of radiation intensity with accounting of finite kinematic bounds. We calculate the suppression of $\pi^0$ - spectra with moderate high $p_{\perp}$, which is caused by energy loss of quark and gluon jets. The comparison with suppression of $\pi^0$ reported by PHENIX show, that correct quantitative description of suppression we have only in model of phase transition with decrease of thermal gluon mass and effective coupling $G(T)$ in region of phase transition plasma into hadrons (at $T \simeq T_c$). However quasiparticle model with increase of these values at $T \to T_c$ in accordance with perturbative QCD lead to too great energy loss of gluon and quark jets, which disagrees with data on suppression of $\pi^0$. Thus it is possible with help of hard processes to investigate the structure of phase transition. We show also, that energy losses at SPS energy are too small in order to be observable. This is caused in fact by sufficiently short plasma phase at this energy.Comment: 17 pages, 3 figures, 2 table

Entanglement, identical particles and the uncertainty principle

A new uncertainty relation (UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which explicitly shows the quantum correlations among the particles that constitute the system. For the particular cases of two and three particles, making use of the Schwarz inequality, we obtain new lower bounds for the UR that are different from the standard one.Comment: 5 pages, no figure; v2: title, abstract, and focus slightly changed; a couple of sections rewritten and a new one added; published versio

On Visibility in the Afshar Two-Slit Experiment

A modified version of Young's experiment by Shahriar Afshar indirectly reveals the presence of a fully articulated interference pattern prior to the post-selection of a particle in a "which-slit" basis. While this experiment does not constitute a violation of Bohr's Complementarity Principle as claimed by Afshar, both he and many of his critics incorrectly assume that a commonly used relationship between visibility parameter V and "which-way" parameter K has crucial relevance to his experiment. It is argued here that this relationship does not apply to this experimental situation and that it is wrong to make any use of it in support of claims for or against the bearing of this experiment on Complementarity.Comment: Final version; to appear in Foundations of Physic

Afshar's Experiment does not show a Violation of Complementarity

A recent experiment performed by S. Afshar [first reported by M. Chown, New Scientist {\bf 183}, 30 (2004)] is analyzed. It was claimed that this experiment could be interpreted as a demonstration of a violation of the principle of complementarity in quantum mechanics. Instead, it is shown here that it can be understood in terms of classical wave optics and the standard interpretation of quantum mechanics. Its performance is quantified and it is concluded that the experiment is suboptimal in the sense that it does not fully exhaust the limits imposed by quantum mechanics.Comment: 6 pages, 6 figure

Discrete Dynamics: Gauge Invariance and Quantization

Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and internal symmetries. We describe the main features of the gauge principle relevant to the discrete and finite background. Assuming that continuous phenomena are approximations of more fundamental discrete processes, we discuss -- with the help of a simple illustration -- relations between such processes and their continuous approximations. We propose an approach to introduce quantum structures in discrete systems, based on finite gauge groups. In this approach quantization can be interpreted as introduction of gauge connection of a special kind. We illustrate our approach to quantization by a simple model and suggest generalization of this model. One of the main tools for our study is a program written in C.Comment: 15 pages; CASC 2009, Kobe, Japan, September 13-17, 200

Molecular ratchets - verification of the principle of detailed balance

We argue that the recent experiments of Kelly et. al.(Angew. Chem. Int. Ed. Engl. 36, 1866 (1997)) on molecular ratchets, in addition to being in agreement with the second law of thermodynamics, is a test of the principle of detailed balance for the ratchet. We suggest new experiments, using an asymmetric ratchet, to further test the principle. We also point out methods involving a time variation of the temperature to to give it a directional motion

Metrical Quantization

Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates. All quantization schemes that lead to Hilbert space vectors and Weyl operators---even those that eschew Cartesian coordinates---implicitly contain a metric on a flat phase space. This feature is demonstrated by studying the classical and quantum ``aggregations'', namely, the set of all facts and properties resident in all classical and quantum theories, respectively. Metrical quantization is an approach that elevates the flat phase space metric inherent in any canonical quantization to the level of a postulate. Far from being an unwanted structure, the flat phase space metric carries essential physical information. It is shown how the metric, when employed within a continuous-time regularization scheme, gives rise to an unambiguous quantization procedure that automatically leads to a canonical coherent state representation. Although attention in this paper is confined to canonical quantization we note that alternative, nonflat metrics may also be used, and they generally give rise to qualitatively different, noncanonical quantization schemes.Comment: 13 pages, LaTeX, no figures, to appear in Born X Proceeding

A simple explanation of the non-appearance of physical gluons and quarks

We show that the non-appearance of gluons and quarks as physical particles is a rigorous and automatic result of the full, i.e. nonperturbative, nonabelian nature of the color interaction in quantum chromodynamics. This makes it in general impossible to describe the color field as a collection of elementary quanta (gluons). Neither can a quark be an elementary quantum of the quark field, as the color field of which it is the source is itself a source, making isolated noninteracting quarks, crucial for a physical particle interpretation, impossible. In geometrical language, the impossibility of quarks and gluons as physical elementary particles arises due to the fact that the color Yang-Mills space does not have a constant trivial curvature. In QCD, the particles ``gluons'' and ``quarks'' are merely artifacts of an approximation method (the perturbative expansion) and are simply absent in the exact theory. This also coincides with the empirical, experimental evidence.Comment: 8 pages, Latex (to appear in Can.J.Phys.

Wigner's Spins, Feynman's Partons, and Their Common Ground

The connection between spin and symmetry was established by Wigner in his 1939 paper on the Poincar\'e group. For a massive particle at rest, the little group is O(3) from which the concept of spin emerges. The little group for a massless particle is isomorphic to the two-dimensional Euclidean group with one rotational and two translational degrees of freedom. The rotational degree corresponds to the helicity, and the translational degrees to the gauge degree of freedom. The question then is whether these two different symmetries can be united. Another hard-pressing problem is Feynman's parton picture which is valid only for hadrons moving with speed close to that of light. While the hadron at rest is believed to be a bound state of quarks, the question arises whether the parton picture is a Lorentz-boosted bound state of quarks. We study these problems within Einstein's framework in which the energy-momentum relations for slow particles and fast particles are two different manifestations one covariant entity.Comment: LaTex 12 pages, 3 figs, based on the lectures delivered at the Advanced Study Institute on Symmetries and Spin (Prague, Czech Republic, July 2001

From Trees to Loops and Back

We argue that generic one-loop scattering amplitudes in supersymmetric Yang-Mills theories can be computed equivalently with MHV diagrams or with Feynman diagrams. We first present a general proof of the covariance of one-loop non-MHV amplitudes obtained from MHV diagrams. This proof relies only on the local character in Minkowski space of MHV vertices and on an application of the Feynman Tree Theorem. We then show that the discontinuities of one-loop scattering amplitudes computed with MHV diagrams are precisely the same as those computed with standard methods. Furthermore, we analyse collinear limits and soft limits of generic non-MHV amplitudes in supersymmetric Yang-Mills theories with one-loop MHV diagrams. In particular, we find a simple explicit derivation of the universal one-loop splitting functions in supersymmetric Yang-Mills theories to all orders in the dimensional regularisation parameter, which is in complete agreement with known results. Finally, we present concrete and illustrative applications of Feynman's Tree Theorem to one-loop MHV diagrams as well as to one-loop Feynman diagrams.Comment: 52 pages, 17 figures. Some typos in Appendix A correcte