Gravitomagnetic moments of the fundamental fields

The quadratic form of the Dirac equation in a Riemann space-time yields a gravitational gyromagnetic ratio κ(S) = 2 for the interaction of a Dirac spinor with curvature. A gravitational gyromagnetic ratio κ(S) = 1 is also found for the interaction of a vector field with curvature. It is shown that the Dirac equation in a curved background can be obtained as the square-root of the corresponding vector field equation only if the gravitational gyromagnetic ratios are properly taken into account.

Neutrino oscillation in Weitzenbock space-time

In the framework of the teleparallel equivalent of general relativity, we obtain the evolution equation of the neutrino oscillation in vacuum. A comparison with the equivalent result of general relativity case, shows that the Dirac equation in Riemann and Weitzenbock space-times is equivalent in the spherical symmetric Schwarzschild space-time, but turns out to be different in the case of the axial symmetry.

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.

Galilean covariance and non-relativistic Bhabha equations

We apply a five-dimensional formulation of Galilean covariance to construct non-relativistic Bhabha first-order wave equations which, depending on the representation, correspond either to the well known Dirac equation (for particles with spin 1/2) or the Duffin-Kemmer-Petiau equation (for spinless and spin 1 particles). Here the irreducible representations belong to the Lie algebra of the 'de Sitter group' in 4 + 1 dimensions, SO(5, 1). Using this approach, the non-relativistic limits of the corresponding equations are obtained directly, without taking any low-velocity approximation. As a simple illustration, we discuss the harmonic oscillator.

Confinement and soliton solutions in the SL(3) Toda model coupled to matter fields

We consider an integrable conformally invariant two-dimensional model associated to the affine Kac-Moody algebra sl3(ℂ). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U(1) vector current and a topological current, which leads to a confinement of the spinors inside the solitons. We calculate the one-soliton and two-soliton solutions using a procedure which is a hybrid of the dressing and Hirota methods. The soliton masses and time delays due to the soliton interactions are also calculated. We give a computer program to calculate the soliton solutions. © 2002 Published by Elsevier Science B.V.

Scaling limit of virtual states of triatomic systems

Natural scales determine the physics of quantum few-body systems with short-range interactions. Thus, the scaling limit is found when the ratio between the scattering length and the interaction range tends to infinity, while the ratio between the physical scales are kept fixed. From the formal point of view, the relation of the scaling limit and the renormalization aspects of a few-body model with a zero-range interaction, through the derivation of subtracted three-body T-matrix equations that are renormalization-group invariant.

Scaling predictions for radii of weakly bound triatomic molecules

The mean-square radii of the triatomic molecules 4He 3, 4He 2- 6Li, 4He 2- 7Li, and 4He 2- 23Na were calculated using a renormalized three-body model with a pairwise Dirac-δ interaction, having as physical inputs only the values of the binding energies of the diatomic and triatomic molecules. Molecular three-body systems with bound subsystems were considered. The resultant data were analyzed in detail.

Higher grading conformal affine Toda theory and (generalized) sine-Gordon/massive Thirring duality

Some properties of the higher grading integrable generalizations of the conformal affine Toda systems are studied. The fields associated to the non-zero grade generators are Dirac spinors. The effective action is written in terms of the Wess-Zumino-Novikov-Witten (WZNW) action associated to an affine Lie algebra, and an off-critical theory is obtained as the result of the spontaneous breakdown of the conformal symmetry. Moreover, the off-critical theory presents a remarkable equivalence between the Noether and topological currents of the model. Related to the off-critical model we define a real and local lagrangian provided some reality conditions are imposed on the fields of the model. This real action model is expected to describe the soliton sector of the original model, and turns out to be the master action from which we uncover the weak-strong phases described by (generalized) massive Thirring and sine-Gordon type models, respectively. The case of any (untwisted) affine Lie algebra furnished with the principal gradation is studied in some detail. The example of s^l(n) (n = 2, 3) is presented explicitly. © SISSA/ISAS 2003.

Pseudospin symmetry and the relativistic harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r. Setting either or both combinations Σ=5+V and δ=V-S to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the nonrelativistic limit and the case Σ=0, for which pseudospin symmetry is exact. We also show that the case U=δ=0 is the most natural generalization of the nonrelativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic-oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the relativistic harmonic oscillator in the pseudospin limit.

Quantum topology change and large-N gauge theories

We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection X of N one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator D. The set of boundary conditions encodes the topology and is parameterized by unitary matrices g. A particular geometry is described by a spectral triple x(g) = (A X, script H sign X, D(g)). We define a partition function for the sum over all g. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. The model has one free-parameter β and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at β = ∞ for any value of N. Moreover, the system undergoes a third-order phase transition at β = 1 for large-N. We give a topological interpretation of the phase transition by looking how it affects the topology. © SISSA/ISAS 2004.

The surface geometry of exotic nuclei

We analyze the surface geometry of the spherical even-even Ca, Ni, Sn and Pb nuclei using two approaches: The relativistic Dirac-Hartree-Bogoliubov one with several parameter sets and the non-relativistic Hartree-Fock-Bogoliubov one with the Gogny force. The proton and neutron density distributions are fitted to two-parameter Fermi density distributions to obtain the half-density radii and diffuseness parameters. Those parameters allow us to determine the nature of the neutron skins predicted by the models. The calculations are compared with existing experimental data. © 2007 American Institute of Physics.

Spin and pseudospin symmetries and the equivalent spectra of relativistic spin-1/2 and spin-0 particles

We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar potentials. The conclusions do not depend on the particular shapes of the potentials and can be important in different fields of physics. When both scalar and vector potentials are spherical, these conditions for isospectrality imply that the spin-orbit and Darwin terms of either the upper component or the lower component of the Dirac spinor vanish, making it equivalent, as far as energy is concerned, to a spin-0 state. In this case, besides energy, a scalar particle will also have the same orbital angular momentum as the (conserved) orbital angular momentum of either the upper or lower component of the corresponding spin-1/2 particle. We point out a few possible applications of this result. © 2007 The American Physical Society.

The Schwinger model on the null-plane

We study the Schwinger Model on the null-plane using the Dirac method for constrained systems. The fermion field is analyzed using the natural null-plane projections coming from the γ-algebra and it is shown that the fermionic sector of the Schwinger Model has only second class constraints. However, the first class constraints are exclusively of the bosonic sector. Finally, we establish the graded Lie algebra between the dynamical variables, via generalized Dirac bracket in the null-plane gauge, which is consistent with every constraint of the theory. © World Scientific Publishing Company.

Statistical quark models for the nucleon structure functions

We consider some existing relativistic models for the nucleon structure functions, relying on statistical approaches instead of perturbative ones. These models are based on the Fermi-Dirac distribution for the confined quarks, where a density of energy levels is obtained from an effective confining potential. In this context, it is presented some results obtained with a recent statistical quark model for the sea-quark asymmetry in the nucleon. It is shown, within this model, that experimental available observables, such as the ratio and difference between proton and neutron structure functions, are quite well reproduced with just three parameters: two chemical potentials used to reproduce the valence up and down quark numbers in the nucleon, and a temperature that is being used to reproduce the Gottfried sum rule violation. © 2010 American Institute of Physics.

Nonpertubative solutions of massless gauged thirring model

We present a nonperturbative quantization of the two-dimensional massless gauged Thirring model by using the path-integral approach. First, we will study the constraint structure of model via the Dirac's formalism and by using the Faddeev-Senjanovic method we calculate the vacuum-vacuum transition amplitude in a Rξ-gauge, then we compute the Green's functions in a nonperturbative framework. © 2010 American Institute of Physics.