International Journal of Modern Physics A

We study the classical dynamics of nonrelativistic particles endowed with spin. Nonvanishing Zitterbewegung terms appear in the equation of motion also in the small momentum limit. We derive a generalized work-energy theorem which suggests classical interpretations for tunnel effect and quantum potential.

We study a five-dimensional cosmological model, which suggests that the universe began as a discontinuity in a scalar (Higgs-type) field, or alternatively as a conventional four-dimensional phase transition.

Λ⁰ polarization (P) depends on x_f and p_t; it depends also on the density of the target material: P(x_f, p_t, ρ) = (κ₀/(λ₀ + ρ/ρ_w))x_fp_t, with κ₀ = -0.423±0.065 (GeV/c)^-1 and λ₀ = 1.191±0.200 in the range 0<p_t<1.2 GeV. Here ρ is the target material density and ρ_w is the Tungsten density. From this equation, it follows that Λ⁰ polarization is reduced by target density.

We begin with a discussion on two apparently disconnected topics — one related to nonperturbative superpotential generated from wrapping an M2-brane around a supersymmetric three cycle embedded in a G₂-manifold evaluated by the path-integral inside a path-integral approach of Ref. 1, and the other centered around the compact Calabi–Yau CY₃(3, 243) expressed as a blow-up of a degree-24 Fermat hypersurface in WCP⁴[1, 1, 2, 8, 12]. For the former, we compare the results with the ones of Witten on heterotic worldsheet instantons.² The subtopics covered in the latter include an 𝒩=1 triality between Heterotic, M- and F-theories, evaluation of RP²-instanton superpotential, Picard–Fuchs equation for the mirror Landau–Ginzburg model corresponding to CY₃(3, 243), D = 11 supergravity corresponding to M-theory compactified on a "barely" G₂ manifold involving CY₃(3, 243) and a conjecture related to the action of antiholomorphic involution on period integrals. We then shown an indirect connection between the two topics by showing a connection between each one of the two and Witten's MQCD.³ As an aside, we show that in the limit of vanishing "ζ", a complex constant that appears in the Riemann surfaces relevant to defining the boundary conditions for the domain wall in MQCD, the infinite series of Ref. 4 used to represent a suitable embedding of a supersymmetric 3-cycle in a G₂-mannifold, can be summed.

We have calculated the perturbative corrections to all the structure functions in the semileptonic decays of a heavy quark. Assuming an arbitrary gluon mass as a technical tool allowed to obtain in parallel all the BLM corrections. We report the basic applications, viz. perturbative corrections to the hadronic mass and energy moments with full dependence on the charge lepton energy cut. In the adopted scheme with the OPE momentum scale separation around 1 GeV the perturbative corrections to are small and practically independent of E_cut; the BLM corrections are small, too. The corrections to the second mass squared moment show some decrease with E_cut consistent with the effect of the Darwin operator, within the previously estimated theoretical uncertainty. Perturbative corrections in the pole-type schemes appear significant and vary with E_ℓ, decreasing the moments at higher cuts. The hardness of hadronic moments is quantitatively illustrated for different cuts on E_ℓ.

By using the Jacobi metric of the configuration space, and assuming ergodicity, we calculate the Boltzmann entropy S of a finite-dimensional system around a nondegenerate critical point of its potential energy V. We compare S with the entropy of a quantum or thermal system with effective potential V_eff. We examine conditions, up to first order in perturbation theory, under which these entropies are equal.

In this paper, we explicitly derive the generalized mirror transformation of quantum cohomology of general type projective hypersurfaces, proposed in our previous article, as an effect of coordinate change of the virtual Gauss–Manin system.

We discuss the vacuum energy density and the cosmological constant of dS₅ brane-world with a dilaton field. It is shown that a stable AdS₄ brane can be constructed and gravity localization can be realized. An explicit relation between the dS bulk cosmological constant and the brane cosmological constant is obtained. The discrete mass spectrum of the massive scalar field in the AdS₄ brane is used to acquire the relationship between the brane cosmological constant and the vacuum energy density. The vacuum energy density in the brane gotten by this method is in agreement with astronomical observations.

Using the Bergmann–Thomson energy–momentum complex and its tele-parallel gravity version, we obtain the energy and momentum of the universe in viscous Kasner-type cosmological models. The energy and momentum components (due to matter plus field) are found to be zero and this agree with a previous work of Rosen and Johri et al. who investigated the problem of the energy in Friedmann–Robertson–Walker universe. The result that the total energy and momentum components of the universe in these models is zero supports the viewpoint of Tryon. Rosen found that the energy of the Friedmann–Robertson–Walker space–time is zero, which agrees with the studies of Tryon.

The study of recently introduced Fedosov supermanifolds¹ is continued. Using normal coordinates, properties of even and odd symplectic supermanifolds endowed with a symmetric connection respecting given sympletic structure are studied.

We would like to present some exact SU(2) Yang–Mills–Higgs monopole solutions of half-integer topological charge. These solutions can be just an isolated half-monopole or a multimonopole with topological magnetic charge ½m where m is a natural number. These static monopole solutions satisfy the first order Bogomol'nyi equations. The axially symmetric one-half monopole gauge potentials possess a Dirac-like string singularity along the negative z-axis. The multimonopole gauge potentials are also singular along the z-axis and possess only mirror symmetries.