Simple derivation of general Fierz-type identities

General Fierz-type identities are examined and their well known connection with completeness relations in matrix vector spaces is shown. In particular, I derive the chiral Fierz identities in a simple and systematic way by using a chiral basis for the complex $4\times4$ matrices. Other completeness relations for the fundamental representations of SU(N) algebras can be extracted using the same reasoning.Comment: 9pages. Few sentences modified in introduction and in conclusion. Typos corrected. An example added in introduction. Title modifie

Quantum Determinism from Quantum General Covariance

The requirement of general covariance of quantum field theory (QFT) naturally leads to quantization based on the manifestly covariant De Donder-Weyl formalism. To recover the standard noncovariant formalism without violating covariance, fields need to depend on time in a specific deterministic manner. This deterministic evolution of quantum fields is recognized as a covariant version of the Bohmian hidden-variable interpretation of QFT.Comment: 6 pages, revised, new references, Honorable Mention of the Gravity Research Foundation 2006 Essay Competition, version to appear in Int. J. Mod. Phys.

Structure Functions in Deep Inelastic Lepton-Nucleon Scattering

Latest results on structure functions, as available at the Lepton-Photon Symposium 1999, are presented. This report focusses on three experimental areas: new structure function measurements, in particular from HERA at low x and high Q2; results on light and heavy flavour densities; determinations of the gluon distribution and of alpha_s. As the talk was delivered at a historic moment and place, a few remarks were added recalling the exciting past and looking into the promising future of deep inelastic scattering.Comment: 27 pages, latex, 15 figures, Talk at Lepton-Photon Symposium, Stanford, August 199

B→D∗∗B\to D^{\ast\ast} semileptonic decay in covariant quark models \`a la Bakamjian Thomas

Once chosen the dynamics in one frame, for example the rest frame, the Bakamjian and Thomas method allows to define relativistic quark models in any frame. These models have been shown to provide, in the heavy quark limit, fully covariant current form factors as matrix elements of the quark current operator. They also verify the Isgur-Wise scaling and give a slope parameter $\rho^2>3/4$ for all the possible choices of the dynamics. In this paper we study the $L=1$ excited states and derive the general formula, valid for any dynamics, for the scaling invariant form factors $\tau_{1/2}^{(n)}(w)$ and $\tau_{3/2}^{(n)}(w)$. We also check the Bjorken-Isgur-Wise sum rule already demonstrated elsewhere in this class of models.Comment: 14 pages, Latex2e, AMS-LaTe

Ridge Formation Induced by Jets in pppp Collisions at 7 TeV

An interpretation of the ridge phenomenon found in pp collisions at 7 TeV is given in terms of enhancement of soft partons due to energy loss of semihard jets. A description of ridge formation in nuclear collisions can directly be extended to pp collisions, since hydrodynamics is not used, and azimuthal anisotropy is generated by semihard scattering. Both the p_T and multiplicity dependencies are well reproduced. Some suggestions are made about other observables.Comment: Expanded version to be published in Phys. Rev.

Cluster Structure of Disoriented Chiral Condensates in Rapidity Distribution

We study the creation of disoriented chiral condensates with some initial boundary conditions that may be expected in the relativistic heavy ion collisions. The equations of motion in the linear $\sigma$-model are solved numerically with and without a Lorentz-boost invariance. We suggest that a distinct cluster structure of coherent pion production in the rapidity distribution may emerge due to a quench and may be observed in experiments.Comment: 10 pages in LaTex, 2 uuencoded ps figures, LBL-3493

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.

Explicit form of the Isgur-Wise function in the BPS limit

Using previously formulated sum rules in the heavy quark limit of QCD, we demonstrate that if the slope rho^2 = -xi'(1) of the Isgur-Wise function xi(w) attains its lower bound 3/4, then all the derivatives (-1)^L xi^(L)(1) attain their lower bounds (2L+1)!!/2^(2L), obtained by Le Yaouanc et al. This implies that the IW function is completely determined, given by the function xi(w) = [2/(w+1)]^(3/2). Since the so-called BPS condition proposed by Uraltsev implies rho^2 = 3/4, it implies also that the IW function is given by the preceding expression.Comment: 19 page

Charmed Mesons Have No Discernable Color-Coulomb Attraction

Starting with a confining linear Lorentz scalar potential V_s and a Lorentz vector potential V_v which is also linear but has in addition a color-Coulomb attraction piece, -alpha_s/r, we solve the Dirac equation for the ground-state c- and u-quark wave functions. Then, convolving V_v with the u-quark density, we find that the Coulomb attraction mostly disappears, making an essentially linear barV_v for the c-quark. A similar convolution using the c-quark density also leads to an essentially linear tildeV_v for the u-quark. For bound cbar-c charmonia, where one must solve using a reduced mass for the c-quarks, we also find an essentially linear widehatV_v. Thus, the relativistic quark model describes how the charmed-meson mass spectrum avoids the need for a color-Coulomb attraction.Comment: 9 pages, 5 PDF figure