Three-particle poincaré states and SU(6) × SU(3) as a classification group for baryons

A complete set of democratic quantum numbers is introduced to classify the states of an irreducible unitary representation (IUR) of the Poincaré group obtained from the decomposition of the direct product of three IUR. Such states are identified with the baryon states constituted of three free relativistic quarks. The transformation from current to constituent quarks is then easily reobtained. Moreover, the group SU(6) × SU(3) appears naturally as a collinear classification group for baryons. Results similar to those of the symmetric harmonic oscillator quark model are obtained.     

Modal-Hamiltonian Interpretation of Quantum Mechanics and Casimir Operators: The Road Toward Quantum Field Theory

The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) fields. In this case we propose that the actual-valued observables are the Casimir operators of the Poincaré group and of the group U(1) of the internal symmetry of the theory. Moreover, we also show that the magnitudes that acquire actual values in the relativistic and in the non-relativistic cases are correctly related through the adequate limit.     

Bi-local baryon interpolating fields with two flavors

We construct bi-local interpolating field operators for baryons consisting of three quarks with two flavors, assuming good isospin symmetry. We use the restrictions following from the Pauli principle to derive relations/identities among the baryon operators with identical quantum numbers. Such relations that follow from the combined spatial, Dirac, color, and isospin Fierz transformations may be called the (total/complete) Fierz identities. These relations reduce the number of independent baryon operators with any given spin and isospin. We also study the Abelian and non-Abelian chiral transformation properties of these fields and place them into baryon chiral multiplets. Thus we derive the independent baryon interpolating fields with given values of spin (Lorentz group representation), chiral symmetry (U _L (2)×U _R (2) group representation) and isospin appropriate for the first angular excited states of the nucleon.     

Baryon-vector-meson couplings in a quark model with chromodynamics

The couplings of baryons to channels involving a vector meson and a ground-state baryon in the final state are calculated for states associated with up to two orbital or one radial excitation in the non-relativistic quark model. These amplitudes are then combined with the baryon compositions predicted by a quark model incorporating some of the features expected to arise from quantum chromodynamics. A comparison with experiment is made.     

Complex geometry,unification, and quantum gravity. I. The geometry of elementary particles

The Poincaré group is replaced byU(3, 2), the pseudounitary extension of the de Sitter groupSO(3, 2), as internal and space-time symmetries are combined in a geometric setting which invalidates the no-go theorems. A new model of elementary particles as vertical vectors on the principal fiber bundleU(3, 2) U(3, 2)/U(3, 1)×U(1) is introduced and their interactions via Lie bracket analyzed. The model accounts for the four known superselection rules: spin, electric charge, baryon number, and lepton number.     

Spinor-electron wave guided modes in coupled quantum wells structures by solving the Dirac equation

A quantum analysis based on the Dirac equation of the propagation of spinor-electron waves in coupled quantum wells, or equivalently coupled electron waveguides, is presented. The complete optical wave equations for Spin-Up (SU) and Spin-Down (SD) spinor-electron waves in these electron guides couplers are derived from the Dirac equation. The relativistic amplitudes and dispersion equations of the spinor-electron wave-guided modes in a planar quantum coupler formed by two coupled quantum wells, or equivalently by two coupled slab electron waveguides, are exactly derived. The main outcomes related to the spinor modal structure, such as the breaking of the non-relativistic degenerate spin states, the appearance of phase shifts associated with the spin polarization and so on, are shown.     

The axial form factor in the Nambu-Jona-Lasinio model

We give a general expression for the expectation value of the axial vector currentA _µ ^a in a system with baryon numberB=1, which arises as solution of theSU(2)—flavour Nambu-Jona-Lasinio model in the fermion-1-loop approximation. States with good spin and isospin quantum numbers are constructed by using the lowest order cranking approximation. Taking the self consistent solutions for such a system we calculate the axial form factorg _A(q ²) and the axial coupling constantg _A . The results can be checked by comparing the value of g_A with the one obtained from the radial integral or the asymptotic tail of the self consistent pion field by means of the PCAC relation.     

Electromagnetic transitions of low-lying nucleon resonances in point form relativistic quantum mechanics

Point form relativistic quantum mechanics is employed to calculate the electromagnetic transition amplitudes of low-lying nucleon resonances. The results obtained are compared with the non-relativistic approach and other model calculations. Differences among them are discussed.     

A strong interaction theory with internal coordinates

Quantum theory andSU ₃ classification of hadrons are partially unified and are extended to produce a single formalism. The theory accounts for the possibility that a number of different hardrons can be exchanged between two quarks without explicitly assuming their masses and quantum numbers. Quantization of the theory leads to the conclusion that a quark has spin 1/2 but obeys Bose statistics and naturally accounts for the relation between spin and statistics for the baryon decuplet.     

Helicity amplitudes and electromagnetic decays of hyperon resonances

We present results for the helicity amplitudes of the lowest-lying hyperon resonances Y^*, computed within the framework of the Bonn Constituent-Quark model, which is based on the Bethe-Salpeter approach. The seven parameters entering the model were fitted to the best-known baryon masses. Accordingly, the results for the helicity amplitudes are genuine predictions. Some hyperon resonances are seen to couple more strongly to a virtual photon with finite Q² than to a real photon. Other Y^*'s, such as the S₀₁(1670) Λ-resonance or the S₁₁(1620) Σ-resonance, couple very strongly to real photons. We present a qualitative argument for predicting the behaviour of the helicity asymmetries of baryon resonances at high Q².-1     

Spin in kink-type field theories

This paper studies some classical three-dimensional field theories for which the ranges of the field variables are a 3-sphere, a 2-sphere, the symplectic group,Sp(n), the special orthogonal group,SO(3), and theS _4,1 space of general relativistic metrics. The main result is the proof that these theories admit half-odd-integer spin, so that the 1-kink states are classical analogs of fermion states.     

Spin-related phenomena in InAs/GaSb quantum wells

We have studied theoretically the influence of symmetry breaking mechanisms: structural inversion asymmetry, bulk inversion asymmetry, relativistic and non-relativistic interface Hamiltonian and warping on spin split of levels ΔE and optical absorption of linearly polarized light in asymmetrical quantum wells made from zincblende materials grown on [001] direction. The AlSb/InAs/GaSb/AlSb broken-gap quantum wells with hybridized electron-hole states sandwiched by the AlSb barriers have been considered. We have obtained substantial contributions of these effects into the absolute values of spin split of electron and hole states and spinflip optical transitions for the initial state in-plane wave vectors along low symmetry directions such as [12].     

Dispersion theory and the low-energy constants for neutral-pion photoproduction

The relativistic amplitudes of pion photoproduction are evaluated by dispersion relations at t = const. The imaginary parts of the amplitudes are taken from the MAID model covering the absorption spectrum up to center-of-mass energies W = 2.2GeV. For sub-threshold kinematics the amplitudes are expanded in powers of the two independent variables ν and t related to energy and momentum transfer. Subtracting the loop corrections from this power series allows one to determine the counter terms of covariant baryon chiral perturbation theory. The proposed continuation of the amplitudes into the unphysical region provides a unique framework to derive the low-energy constants to any given order as well as an estimate of the higher-order terms by global properties of the absorption spectrum.     

A Study of Electromagnetic Transition of △（1232） Resonance

Point form relativistic dynamics of relativistic quantum mechanics is employed to estimate the photon and electroproduction amplitudes of A(1232) resonance. Results are compared with the non-relativistic work, and the differences between the two frame works are discussed.     

Relativistic corrections to the baryon resonance photoexcitation amplitudes in the quark model

We calculate the relativistic corrections of order (quark mass)^?2 to the baryon resonance photoexcitation amplitudes in the harmonic-oscillator quark model. We find that the relativistic effects entail significant consequences and that the agreement with experiment is much improved.     

Unrestricted Dirac-Fock theory: Relativistic determination of core polarization hyperfine interactions

The unrestricted Dirac-Fock (UDF) method is developed for determining relativistic contributions to the hyperfine interaction, notably that due to core polarization. Radial core-polarization of the one-electron (jj-coupled) spin orbitals is obtained by relaxing the restraint in restricted Dirac-Fock (RDF) theory that the radial part be independent of the magnetic quantum number, the projection m_j of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock (m_s unrestricted) and spin plus orbital polarized Hartree- Fock (m_s plus m_j unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, S_s(z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (≈6) found earlier for these same ions. Comparison is made with limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment.     

The second EMC effect,semileptonic baryon decays and the chiral bag

TheU(1) anomaly gives a massiveη ₀ in the chiralSU(3) limit. We show in this limit how a chiral bag model givesboth theF andD amplitudes consistent with all baryon semileptonic decays,and the integral over the spin structure function measured by the EMC collaboration.