Unitary Operator Bases and Q-deformed Algebras

Starting from the Schwinger unitary operator bases formalism constructed out of a finite dimensional state space, the well-known q-deformed commutation relation is shown to emerge in a natural way, when the deformation parameter is a root of unity.

Leading particle effect, inelasticity, and the connection between average multiplicities in e+e- and pp processes

The Regge-Mueller formalism is used to describe the inclusive spectrum of the proton in pp collisions. From such a description the energy dependences of both average inelasticity and leading proton multiplicity are calculated. These quantities are then used to establish the connection between the average charged particle multiplicities measured in e+e- and pp/p̄p processes. The description obtained for the leading proton cross section implies that Feynman scaling is strongly violated only at the extreme values of xF, that is at the central region (xF≈0) and at the diffraction region (XF≈1), while it is approximately observed in the intermediate region of the spectrum. ©1999 The American Physical Society.

Feynman integrals with tensorial structure in the negative dimensional integration scheme

The negative-dimensional integration method (NDIM) is revealing itself as a very useful technique for computing massless and/or massive Feynman integrals, covariant and noncovanant alike. Up until now however, the illustrative calculations done using such method have been mostly covariant scalar integrals/without numerator factors. We show here how those integrals with tensorial structures also can be handled straightforwardly and easily. However, contrary to the absence of significant features in the usual approach, here the NDIM also allows us to come across surprising unsuspected bonuses. Toward this end, we present two alternative ways of working out the integrals and illustrate them by taking the easiest Feynman integrals in this category that emerge in the computation of a standard one-loop self-energy diagram. One of the novel and heretofore unsuspected bonuses is that there are degeneracies in the way one can express the final result for the referred Feynman integral.

Inelastic photoproduction at HERA: A second charmonium crisis?

Measurements of the inelastic photoproduction of charmonium at HERA have ignited a new charmonium crisis. The Color Singlet approach to computing onium production cross sections fits the data for large charmonium energy fraction z, where color octet models fail. This approach is however in qualitative disagreement with a wealth of information that exist on charmonium production by other initial states. We here suggest that the source of the discrepancy between color octet models (whether implemented in the soft color or NRQCD formalism) and data is due to the neglect of non-perturbative effects. Implementing these in a scheme originally developed for Drell-Yan phenomenology, we illustrate how agreement with the data is achieved. © 1999 Elsevier Science B.V. All rights reserved.

Conformai field theory of AdS background with Ramond-Ramond flux

We review a formalism of superstring quantization with manifest six-dimensional spacetime supersymmetry, and apply it to AdS3 × S3 backgrounds with Ramond-Ramond flux. The resulting description is a conformal field theory based on a sigma model whose target space is a certain supergroup SU′(2|2).

Deformed Gaussian orthogonal ensemble and the statistical fluctuations in the spectra of the quartic oscillator

The nearest-neighbor spacing distributions proposed by four models, namely, the Berry-Robnik, Caurier-Grammaticos-Ramani, Lenz-Haake, and the deformed Gaussian orthogonal ensemble, as well as the ansatz by Brody, are applied to the transition between chaos and order that occurs in the isotropic quartic oscillator. The advantages and disadvantages of these five descriptions are discussed. In addition, the results of a simple extension of the expression for the Dyson-Mehta statistic Δ3 are compared with those of a more popular one, usually associated with the Berry-Robnik formalism. ©1999 The American Physical Society.

Exploring a rheonomic system

A simple and illustrative rheonomic system is explored in the Lugrangian formalism. The difference between the Jacobi integral and the energy is highlighted. A sharp contrast with remarks found in the literature is pointed out. The non-conservative system possesses a Lagrangian that is not explicitly dependent on time and consequently there is a Jacobi integral. The Lagrange undetermined multiplier method is used as a complement to obtain a few interesting conclusions.

Interference phenomenon for the Faddeevian regularization of 2D chiral fermionic determinants

The classification of the regularization ambiguity of a 2D fermionic determinant in three different classes according to the number of second-class constraints, including the new Faddeevian regularization, is examined and extended. We find a new and important result that the Faddeevian class, with three second-class constraints, possesses a free continuous one parameter family of elements. The criterion of unitarity restricts the parameter to the same range found earlier by Jackiw and Rajaraman for the two-constraint class. We studied the restriction imposed by the interference of right-left modes of the chiral Schwinger model (χQED2) using Stone's soldering formalism. The interference effects between right and left movers, producing the massive vectorial photon, are shown to constrain the regularization parameter to belong to the four-constraint class which is the only nonambiguous class with a unique regularization parameter. ©1999 The American Physical Society.

Induced variational method from supersymmetric quantum mechanics and the screened Coulomb potential

The formalism of supersymmetric quantum mechanics supplies a trial wave function to be used in the variational method. The screened Coulomb potential is analyzed within this approach. Numerical and exact results for energy eigenvalues are compared.

BFFT quantization and dynamical solutions of a fluid field theory

We study a field theory formulation of a fluid mechanical model. We implement the Hamiltonian formalism by using the BFFT conjecture in order to build a gauge invariant fluid field theory. We also generalize previous known classical dynamical field solutions for the fluid model. ©2000 The American Physical Society.

Variation in mandible shape in Thrichomys apereoides (Mammalia: Rodentia): Geometric analysis of a complex morphological structure

The model of development and evolution of complex morphological structures conceived by Atchley and Hall in 1991 (Biol. Rev. 66:101-157), which establishes that changes at the macroscopic, morphogenetic level can be statistically detected as variation in skeletal units at distinct scales, was applied in combination with the formalism of geometric morphometrics to study variation in mandible shape among populations of the rodent species Thrichomys apereoides. The thin-plate spline technique produced geometric descriptors of shape derived from anatomical landmarks in the mandible, which we used with graphical and inferential approaches to partition the contribution of global and localized components to the observed differentiation in mandible shape. A major pattern of morphological differentiation in T. apereoides is attributable to localized components of shape at smaller geometric scales associated with specific morphogenetic units of the mandible. On the other hand, a clinal trend of variation is associated primarily with localized components of shape at larger geometric scales. Morphogenetic mechanisms assumed to be operating to produce the observed differentiation in the specific units of the mandible include mesenchymal condensation differentiation, muscle hypertrophy, and tooth growth. Perspectives for the application of models of morphological evolution and geometric morphometrics to morphologically based systematic biology are considered.

Nonforward parton distributions of the pion within an effective single instanton approximation

We develop a relativistic quark model for pion structure, which incorporates the nontrivial structure of the vacuum of quantum chromodynamics as modelled by instantons. Pions are bound states of quarks and the strong quark-pion vertex is determined from an instanton induced effective Lagrangian. The interaction of the constituents of the pion with the external electromagnetic field is introduced in gauge invariant form. The parameters of the model, i.e., effective instanton radius and constituent quark mass, are obtained from the vacuum expectation values of the lowest dimensional quark and gluon operators and the low-energy observables of the pion. We apply the formalism to the calculation of the pion form factor by means of the isovector nonforward parton distributions and find agreement with the experimental data. © 2000 Elsevier Science B.V.

Renormalization of the ladder light-front Bethe-Salpeter equation in the Yukawa model

The reduction of the two-fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded in powers of the coupling constant gs allowing a defined number of boson exchanges; it is divergent and needs renormalization; it also includes the instantaneous term of the Dirac propagator. One possible solution of the renormalization problem of the boson exchanges is shown to be provided by expanding the effective interaction beyond single boson exchange. The effective interaction in ladder approximation up to order g4 s is discussed in detail. It is shown that the effective interaction naturally yields the box counterterm required to be introduced ad hoc previously. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional quantities.

Quantum vacuum in hot nuclear matter: A non-perturbative treatment

We derive the equation of state for hot nuclear matter using the Walecka model in a non-perturbative formalism. We include here the vacuum polarization effects arising from the nucleon and scalar mesons through a realignment of the vacuum. A ground state structure with baryon-antibaryon condensates yields the results obtained through the relativistic Hartree approximation of summing baryonic tadpole diagrams. Generalization of such a state to include the quantum effects for the scalar meson fields through the σ -meson condensates amounts to summing over a class of multiloop diagrams. The techniques of the thermofield dynamics method are used for the finite-temperature and finite-density calculations. The in-medium nucleon and sigma meson masses are also calculated in a self-consistent manner. We examine the liquid-gas phase transition at low temperatures (≈ 20 MeV), as well as apply the formalism to high temperatures to examine a possible chiral symmetry restoration phase transition.

On the regular-geometric-figure solution to the N-body problem

The regular-geometric-figure solution to the N-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of interactions beyond the gravitational ones for some special values of the parameters of the forces. For the harmonic oscillator, in particular, it is shown that the N-body problem is reduced to N one-body problems.