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.

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.

Relating the RNS and pure spinor formalisms for the superstring

Recently, the superstring was covariantly quantized using the BRST-like operator Q = ∮ λαdα where λα is a pure spinor and dα are the fermionic Green-Schwarz constraints. By performing a field redefinition and a similarity transformation, this BRST-like operator is mapped to the sum of the Ramond-Neveu-Schwarz BRST operator and η0 ghost. This map is then used to relate physical vertex operators and tree amplitudes in the two formalisms. Furthermore, the map implies the existence of a b ghost in the pure spinor formalism which might be useful for loop amplitude computations.

Interference phenomena, chiral bosons, and Lorentz invariance

We have studied the theory of gauged chiral bosons and proposed a general theory, a master action, that encompasses different kinds of gauge field couplings in chiral bosonized theories with first-class chiral constraints. We have fused opposite chiral aspects of this master action using the soldering formalism and applied the final action to several well-known models. The Lorentz rotation permitted us to fix conditions on the parameters of this general theory in order to preserve the relativistic invariance. We also have established some conditions on the arbitrary parameter concerned in a chiral Schwinger model with a generalized constraint, investigating both covariance and Lorentz invariance. The results obtained supplement the one that shows the soldering formalism as a new method of mass generation. ©2001 The American Physical Society.

New remarks on the linear constraint self-dual boson and Wess-Zumino terms

In this work we prove in a precise way that the soldering formalism can be applied to the Srivastava chiral boson (SCB), in contradiction with some results appearing in the literature. We promote a canonical transformation that shows directly that the SCB is composed of two Floreanini-Jackiw particles with the same chirality in which the spectrum is a vacuumlike one. As another conflicting result, we prove that a Wess-Zumino (WZ) term used in the literature consists of a scalar field, once again denying the assertion that the WZ term adds a new degree of freedom to the SCB theory in order to modify the physics of the system. © 2001 The American Physical Society.

Excluded volume effects in the quark meson coupling model

Excluded volume effects are incorporated in the quark-meson coupling model to take into account in a phenomenological way the hard-core repulsion of the nuclear force. The formalism employed is thermodynamically consistent and does not violate causality. The effects of the excluded volume on in-medium nucleon properties and the nuclear matter equation of state are investigated as a function of the size of the hard core. It is found that in-medium nucleon properties are not altered significantly by the excluded volume, even for large hard-core radii, and the equation of state becomes stiffer as the size of the hard core increases.

Massive superstring vertex operator in D = 10 superspace

Using the pure spinor formalism for the superstring, the vertex operator for the first massive states of the open superstring is constructed in a manifestly super-Poincaré covariant manner. This vertex operator describes a massive spin-two multiplet in terms of ten-dimensional superfields. © SISSA/ISAS 2002.

Towards covariant quantization of the supermembrane

By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d = 10 superparticle and superstring is extended to the d = 11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like invariance using the nilpotent operator Q = ∮ λ αdα where dα is the worldvolume variable corresponding to the d = 11 spacetime supersymmetric derivative and λα is an SO(10, 1) pure spinor variable satisfying λΓcλ = 0 for c = 1 to 11. Super-Poincaré covariant unintegrated and integrated supermembrane vertex operators are explicitly constructed which are in the cohomology of Q. After double-dimensional reduction of the eleventh dimension, these vertex operators are related to type-IIA superstring vertex operators where Q = QL + QR is the sum of the left and right-moving type-IIA BRST operators and the eleventh component of the pure spinor constraint, λΓ 11λ = 0, replaces the bL 0 - b R 0 constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators. © SISSA/ISAS 2002.