Vector and axial-vector correlators in a non-local chiral quark model

The behavior of the non-perturbative parts of the isovector-vector and isovector and isosinglet axial-vector correlators at Euclidean momenta is studied in the framework of a covariant chiral quark model with non-local quark-quark interactions. The gauge covariance is ensured with the help of the P-exponents, with the corresponding modification of the quark-current interaction vertices taken into account. The low- and high-momentum behavior of the correlators is compared with the chiral perturbation theory and with the QCD operator product expansion, respectively. The V-A combination of the correlators obtained in the model reproduces quantitatively the ALEPH and OPAL data on hadronic tau decays, transformed into the Euclidean domain via dispersion relations. The predictions for the electromagnetic pi(+/-) - pi(0) mass difference and for the pion electric polarizability are also in agreement with the experimental values. The topological susceptibility of the vacuum is evaluated as a function of the momentum, and its first moment is predicted to be chi'(0) approximate to (50 MeV)(2). In addition, the fulfillment of the Crewther theorem is demonstrated.

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-Poincare covariant manner. This vertex operator describes a massive spin-two multiplet in terms of ten-dimensional superfields.

The quadratic spinor Lagrangian, axial torsion current and generalizations

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein-Hilbert, Einstein-Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto spinor field classification, that any other class of spinor field-Weyl, Majorana, flagpole, or flag-dipole spinor fields-yields a trivial (zero) QSL, up to a boundary term. To investigate this boundary term, we do not impose any constraint on the Dirac spinor field, and consequently we obtain new terms in the boundary component of the QSL. In the particular case of a teleparallel connection, an axial torsion one-form current density is obtained. New terms are also obtained in the corresponding Hamiltonian formalism. We then discuss how these new terms could shed new light on more general investigations.

The light-cone gauge without prescriptions

Feynman integrals in the physical light-cone gauge are more difficult to solve than their covariant counterparts. The difficulty is associated with the presence of unphysical singularities due to the inherent residual gauge freedom in the intermediate boson propagators constrained within this gauge choice. In order to circumvent these non-physical singularities, the headlong approach has always been to call for mathematical devices - prescriptions - some successful and others not. A more elegant approach is to consider the propagator from its physical point of view, that is, an object obeying basic principles such as causality. Once this fact is realized and carefully taken into account, the crutch of prescriptions can be avoided altogether. An alternative, third approach, which for practical computations could dispense with prescriptions as well as avoiding the necessity of careful stepwise consideration of causality, would be of great advantage. and this third option is realizable within the context of negative dimensions, or as it has been coined, the negative dimensional integration method (NDIM).

Light-cone gauge integrals: prescriptionlessness at two loops

The only calculations performed beyond one-loop level in the light-cone gauge make use of the Mandelstam-Leibbrandt (ML) prescription in order to circumvent the notorious gauge dependent poles. Recently we have shown that in the context of negative dimensional integration method (NDIM) such prescription can be altogether abandoned, at least in one-loop order calculations. We extend our approach, now studying two-loop integrals pertaining to two-point functions. While previous works on the subject present only divergent parts for the integrals, we show that our prescriptionless method gives the same results for them, besides finite parts for arbitrary exponents of propagators. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Quantizing a relativistic free-particle on the light front: some subtle aspects

We use the light-front machinery to study the behavior of a relativistic free particle and obtain the quantum commutation relations from the classical Poisson brackets. We argue that their usual projection onto the light-front coordinates from the covariant commutation relations show that there is an inconsistency in the expected correlation between canonically conjugate variables time x(+) and energy p(-). This incompatibility between canonical conjugate variables in the light front is discussed in the context of Poisson brackets and a suggestion is made on how to avoid it.

Lorentz-violating dilatations in momentum space and some extensions on nonlinear actions of Lorentz-algebra-preserving systems

We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which the nonlinear Lorentz dilatation effects here pointed out may be detectable, are suggested.

On high Q(2) behavior of the pion form factor for transitions gamma*gamma -> pi(0) and gamma*gamma* -> pi(0) within the nonlocal quark-pion model

The behavior of the transition pion form factor for processes gamma (*)gamma --> pi(0) and gamma (*)gamma (*) --> pi(0) at large values of space-like photon momenta is estimated within the nonlocal covariant quark-pion model. It is shown that, in general, the coefficient of the leading asymptotic term depends dynamically on the ratio of the constituent quark mass and the average virtuality of quarks in the vacuum and kinematically on the ratio of photon virtualities. The kinematic dependence of the transition form factor allows us to obtain the relation between the pion light-cone distribution amplitude and the quark-pion vertex function. The dynamic dependence indicates that the transition form factor gamma (*)gamma -->, pi(0) at high momentum transfers is very sensitive to the nonlocality size of nonperturbative fluctuations in the QCD vacuum. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Pion structure in the instanton liquid model

The covariant quark model of the pion based on the effective nonlocal quark-hadron Lagrangian involving nonlocality induced by instanton fluctuations of the QCD vacuum is reviewed. Explicit gauge invariant formalism allows us to construct the conserved vector and axial currents and to demonstrate their consistency with the Ward-Takahashi identities and low-energy theorems. The spontaneous breaking of chiral symmetry results in the dynamic quark mass and the vertex of the quark-pion interaction, both momentum-dependent. The parameters of the instanton vacuum, the average size of the instantons, and the effective quark mass are expressed in terms of the vacuum expectation values of the lowest dimension quark-gluon operators and low-energy pion observables. The transition pion form factor for the processes gamma*gamma --> pi (0) and gamma*gamma* --> pi (0) is analyzed in detail. The kinematic dependence of the transition form factor at high momentum transfers allows one to determine the relationship between the light-cone amplitude of the quark distribution in the pion and the quark-pion vertex function. Its dynamic dependence implies that the transition form factor gamma*gamma --> pi (0) at high momentum transfers is acutely sensitive to the size of the nonlocality of nonperturbative fluctuations in the QCD vacuum. In the leading twist, the distribution amplitude and the distribution function of the valence quarks in the pion are calculated at a low normalization point of the order of the inverse average instanton size rho (-1)(c). The QCD results are evolved to higher momentum transfers and are in reasonable agreement with available experimental data on the pion structure.

Lessons of spin and torsion: Reply to Consistent coupling to Dirac fields in teleparallelism

In reply to the criticism made by Mielke in the preceding Comment on our recent paper, we once again explicitly demonstrate the inconsistency of the coupling of a Dirac field to gravitation in the teleparallel equivalent of general relativity. Moreover, we stress that the mentioned inconsistency is generic for all sources with spin and is by no means restricted to the Dirac field. In this sense the SL(4,R)-covariant generalization of the spinor fields in the teleparallel gravity theory is irrelevant to the inconsistency problem.

The character of pure spinors

The character of holomorphic functions on the space of pure spinors in 10, 11 and 12 dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the superstring. We also derive in a simple way the zero momentum cohomology of the pure spinor BRST operator for the D = 10 and D = 11 superparticle.

Non-planar double-box, massive and massless pentabox Feynman integrals in the negative-dimensional approach

The negative-dimensional integration method is a technique which can be applied, with success, in usual covariant gauge calculations. We consider three two-loop diagrams: the scalar massless non-planar double-box with six propagators and the scalar pentabox in two cases, where six virtual particles have the same mass, and in the case all of them are massless. Our results are given in terms of hypergeometric functions of Mandelstam variables and also for arbitrary exponents of propagators and dimension D.

Pure spinor formalism as an N=2 topological string

Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted (c) over cap = 3 N = 2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincare covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action.

Finite-volume form factors in semi-classical approximation

A semi-classical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the spectral representation of correlation functions in a finite volume. Illustrative examples of the applicability of the method are provided by the sine-Gordon and the broken phi(4) theories in 1 + 1 dimensions. (C) 2003 Elsevier B.V. All rights reserved.

Gravitation and the local symmetry group of space-time

According to general relativity, the interaction of a matter field with gravitation requires the simultaneous introduction of a tetrad field, which is a field related to translations, and a spin connection, which is a field assuming values in the Lie algebra of the Lorentz group. These two fields, however, are not independent. By analyzing the constraint between them, it is concluded that the relevant local symmetry group behind general relativity is provided by the Lorentz group. Furthermore, it is shown that the minimal coupling prescription obtained from the Lorentz covariant derivative coincides exactly with the usual coupling prescription of general relativity. Instead of the tetrad, therefore, the spin connection is to be considered as the fundamental field representing gravitation.