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.

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.

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.

In this contribution, we identify two scenarios for the evolutionary branch cut universe. In the first scenario, the universe evolves continuously from the negative complex cosmological time sector, prior to a primordial singularity, to the positive one, circumventing continuously a branch cut, and no primordial singularity occurs in the imaginary sector, only branch points. In the second scenario, the branch cut and branch point disappear after the realization of the imaginary component of the complex time by means of a Wick rotation, which is replaced by the thermal time. In the second scenario, the universe has its origin in the Big Bang, but the model contemplates simultaneously a mirrored parallel evolutionary universe going backwards in the cosmological thermal time negative sector.A quantum formulation based on the Wheeler-DeWitt equation is sketched and preliminary conclusions are drawn.

In this article, we follow a previously developed theoretical approach, based on the tools of the singular semi-Riemannian geometry, to push the limits of time beyond the primordial spacetime singularity. By complexifying the Friedmann-Lemaître-Robertson-Walker (FLRW) metric and Friedmann's equations, we model a branch cut universe, in which the cosmic FLRW metric scale factor is analytically continued to the complex plane, and becomes equivalent from a conceptual point of view of describing a hypothetical general metric of maximally symmetric and homogeneous superposed multiple universes.

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