International Journal of Modern Physics E

Glueballs are particles whose valence degrees of freedom are gluons and therefore in their description the gauge field plays a dominant role. We review recent results in the physics of glueballs with the aim set on phenomenology and discuss the possibility of finding them in conventional hadronic experiments and in the Quark Gluon Plasma. In order to describe their properties we resort to a variety of theoretical treatments which include, lattice QCD, constituent models, AdS/QCD methods, and QCD sum rules. The review is supposed to be an informed guide to the literature. Therefore, we do not discuss in detail technical developments but refer the reader to the appropriate references.

An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific conditions. A pseudo-complex Schwarzschild solution is constructed, which does not suffer any more by a singularity. The solution indicates a minimal radius for a heavy mass object. Consequences for the redshift and possible signatures for its observation are discussed.

We present a consistent and comprehensive treatise on the foundations of the extended Hamilton–Lagrange formalism — where the dynamical system is parametrized along a general system evolution parameter s, and the time t is treated as a dependent variable t(s) on equal footing with all other configuration space variables qⁱ(s). In the action principle, the conventional classical action L₁dt is then replaced by the generalized action L₁ds, with L and L₁ denoting the conventional and the extended Lagrangian, respectively. It is shown that a unique correlation of L₁ and L exists if we refrain from performing simultaneously a transformation of the dynamical variables. With the appropriate correlation of L₁ and L in place, the extension of the formalism preserves its canonical form.

In the extended formalism, the dynamical system is described as a constrained motion within an extended space. We show that the value of the constraint and the parameter s constitutes an additional pair of canonically conjugate variables. In the corresponding quantum system, we thus encounter an additional uncertainty relation.

As a consequence of the formal similarity of conventional and extended Hamilton–Lagrange formalisms, Feynman's nonrelativistic path integral approach can be converted on a general level into a form appropriate for relativistic quantum physics. In the emerging parametrized quantum description, the additional uncertainty relation serves as the means to incorporate the constraint and hence to finally eliminate the parametrization.

We derive the extended Lagrangian L₁ of a classical relativistic point particle in an external electromagnetic field and show that the generalized path integral approach yields the Klein–Gordon equation as the corresponding quantum description. We furthermore derive the space–time propagator for a free relativistic particle from its extended Lagrangian L₁. These results can be regarded as the proof of principle of the relativistic generalization of Feynman's path integral approach to quantum physics.

A particle rotor model with a quasi-neutron coupled with a triaxially deformed rotor is applied to study signature splitting for bands with intruder orbital ν7/2⁺[633] and nonintruder orbital ν5/2^-[512] in ¹⁷³W. Excellent agreement with the observed energy spectra has been achieved for both bands. Signature splitting for band ν7/2⁺[633], and band ν5/2^-[512] before the onset of signature inversion, is satisfactorily reproduced by introducing the γ degree of freedom. The phase and amplitude of signature splitting in band ν5/2^-[512] are attributed to strong competition between 2f_7/2 and 1h_9/2 components. However, the self-consistent explanation of signature inversion in band ν5/2^-[512] is beyond the present one quasi-neutron coupled with a triaxially deformed rotor.

The shell-correction energy is calculated using the single-particle levels obtained with the folded-Yukawa mean-field potential. Three different ways of evaluation of the shell-correction are compared: the traditional Strutinsky method, the modified prescription by the smearing of the total energy sum in the nucleon number space, and the smoothing of the single-particle energies of occupied states and summing them up. The dependence of these three energies on nuclear elongation is investigated.

We present an analytic formula to extract the longitudinal structure function in the next-to-leading order of the perturbation theory at low x, from the Regge-like behavior of the gluon distribution and the structure function at this limit. In this approach, the longitudinal structure function has the hard-Pomeron behavior. The determined values are compared with the H1 data and MRST model. All results can consistently be described within the framework of perturbative QCD, which essentially show increases as x decreases.

The two-proton separation energy (S_2P) has been studied by describing the pairing correlations using four various approaches: in the pairing between like-particles case with (SBCS) and without (BCS) inclusion of the particle-number projection, as well as in the isovector pairing case with (NP-PROJ) and without (NP) inclusion of the particle-number projection. It has been numerically evaluated for the even–even rare-earth proton-rich nuclei such as Δ_np ≠ 0. Among the four used methods, NP-PROJ is the one that provides the results that are closest to the experimental data when available.

On the other hand, it has been shown that the S_2P values deduced from the four approaches join, for almost all the considered elements, for the highest values of (N - Z). The fact that the BCS and NP (respectively, SBCS and NP-PROJ) values join may be explained by the fact that Δ_np decreases with increasing values of (N - Z). It has also been shown that the BCS and SBCS (respectively, NP and NP-PROJ) values of S_2P are very close because the discrepancy between the projected and unprojected energy values is quasi-constant as a function of the deformation.

Finally, the four used methods lead to the same prediction of the two-proton drip-line position except for the Dysprosium and the Tungsten.

The Gaussian sum rules (GSRs) for the D(1^±) and D_s(1^±) mesons current are obtained by means of Laplacian transformation. Based on it, the GSRs for the mass and the coupling constants of D(1^±) and D_s(1^±) mesons are worked out. Using the standard input of quantum chromodynamics nonperturbative parameters, the corresponding curves and tables are presented. The results are in accordance well with the experimental data, and more well than those from the Borel sum rule approach.

A variational approach using a new wave function to ttμ muonic antisymmetric molecular ion is proposed. This approach requires two terms in the total three-body wave function. The formation and fusion take place by the reason of the existence of the both Coulomb potential and nuclear absorption as the Wood–Saxon shape. The nuclear fusion rates for such levels below tμ(1s)+t threshold are calculated with a high accuracy and a short computation time.

A numerical representation for nuclei is suggested and considered as a basis of a cluster model. The binding energy of the cluster representation of a nucleus is introduced. Basic assumptions of the shell model are obtained as the physical side of the suggested cluster representation. ⁸Be₄-decay to two α-particles and ⁹B₅ decay to two α-particles and proton are interpreted.