A mapping technique is used to derive in the context of constituent quark models effective Hamiltonians that involve explicit hadron degrees of freedom. The technique is based on the ideas of mapping between physical and ideal Fock spaces and shares similarities with the quasiparticle method of Weinberg. Starting with the Fock-space representation of singlehadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, hermitian Hamiltonians with a clear physical interpretation are obtained. Applications and comparisons with other composite-particle formalisms of the recent literature are made using the nonrelativistic quark model. Academic Press

The short-range properties of the kaon-nucleon (KN) interaction are studied within the meson-exchange model of the Jülich group. Specifically, dynamical explanations for the phenomenological short-range repulsion, required in this model for achieving agreement with the empirical KN data, are explored. Evidence is found that contributions from the exchange of a heavy scalar-isovector meson ͓a 0 (980)͔ as well as from genuine quark-gluon exchange processes are needed. Taking both mechanisms into account, a satisfactory description of the KN phase shifts can be obtained without resorting to phenomenological pieces.

Extensively applied to both light and heavy meson decay and standing as one of the most successful strong decay models is the 3 P0 model, in which qq pair production is the dominant mechanism. The pair production can be obtained from the non-relativistic limit of a microscopic interaction Hamiltonian involving Dirac quark fields. The evaluation of the decay amplitude can be performed by a diagrammatic technique for drawing quark lines. In this paper we use an alternative approach which consists in a mapping technique, the Fock-Tani formalism, in order to obtain an effective Hamiltonian starting from same microscopic interaction. An additional effect is manifest in this formalism associated to the extended nature of mesons: bound-state corrections. A corrected 3 P0 is obtained and applied, as an example, to b1 → ωπ and a1 → ρπ decays.

The predictions of General Relativity suggest a universe in which, as we follow time backward, the hotter and the more dense it was, and the more rapidly it was expanding and that, around 13.7 billion years ago, at the extreme gravitational regime of its evolutionary process, the density, temperature, and expansion rate of the universe would start off as infinite. The General Relativity prediction of a singularity in the early universe would impose a limitation to our understanding of the cosmos and gravity, implying loss of logic and of formal consistency and predictability, making it impossible to impose initial conditions. These extreme conditions of the initial state of the universe are very far from our experimental possibilities, and presently, theoretical models allow only speculations about the avoidance of physical singularities or about the physical conditions that circumvented this drastic consequence of General Relativity. Speculations aside, in this study, we follow an analytical line in which we apply the tools of singular semi-Riemannian geometry to push the limits of General Relativity beyond the Big Bang singularity.

Starting from the Fock space representation of hadron bound states in a quark model, a change of representation is implemented by a unitary transformation such that the composite hadrons are redescribed by elementary-particle eld operators. Application of the unitary transformation to the microscopic quark Hamiltonian gives rise to eective hadron-hadron, hadron-quark, and quark-quark Hamiltonians. An eective baryon Hamiltonian is derived using a simple quark model. The baryon Hamiltonian is free of the post-prior discrepancy which usually plagues composite-particle eective i n teractions.