Modern Physics Letters A

The analysis of spinors in 2+2 dimensions is reviewed. The two most basic supersymmetry algebras in this space are considered. In the simpler case, the supersymmetry generators are Majorana spinors. In the other algebra we consider, the supersymmetry generators are Dirac spinors. Consistency with having a positive definite Hilbert space is shown to be impossible in both of these particular cases.

The Universe could be spatially flat, positively curved or negatively curved. Each option has been popular at various times, partly affected by an understanding that models tend to evolve away from flatness. The curvature of the Universe is amenable to measurement, through tests such as the determination of the angles of sufficiently large triangles. The angle subtended by the characteristic scale on the cosmic microwave sky provides a direct test, which has now been realized through a combination of exquisite results from a number of CMB experiments.

After a long and detailed investigation, with many false clues, it now seems that the mystery of the curvature of the Universe is now solved. It is an open and shut case: the Universe is flat!

A general dynamical system approach to classical self-consistent scalar field cosmology is presented in the framework of spatially flat FLRW space–times, for arbitrary potentials and arbitrary non-minimal coupling. We show that these universes cannot undergo chaotic behaviors, thus suggesting a possible new role of inflation in cosmology. An unexpectedly involved topology of the phase-portrait of the cosmological dynamics is exhibited: Dynamically forbidden regions, playing a crucial dynamical role, appear. A new exact critical solution, a heteroclinic orbit, connects two de Sitter inflationary regimes. We suggest a novel intriguing semiclassical cosmogenesis scenario in which the quantized scalar field could tunnel through the classically forbidden region, from the Minkowski space–time towards the nearest classically allowed solution: The critical one.

The metric around a wiggly cosmic string is calculated in the linear approximation of Brans–Dicke theory of gravitation. The equations of motion for relativistic and nonrelativistic particles in this metric are obtained. Light propagation is also studied and it is shown that photon trajectories can be bounded.

We study the inter-relations that exist between the present experimental bounds on the Higgs mass, as obtained from radiative corrections to m_W, and the effective parameters, α_i and Λ. We find that the SM bounds on m_H, arising from a precise determination of the W mass, can be substantially modified by the presence of dimension-six operators which appear in the linear realization of the effective Lagrangian approach. A Higgs mass as heavy as 700 GeV can be allowed for scales of new physics of the order of 1 TeV.

We stress the connection between -algebras and noncanonical Heisenberg algebras. We prove that the known Heisenberg–Weyl algebras for the deformed harmonic oscillators are partial cases of the Lie-admissible -algebras. We also point out the existence of a scale factor which plays an important role for the eigenvalue spectrum and for the generalized uncertainty Heisenberg relation. This factor has the form (Δx)(Δp) ≥ ℏ′/2 with ℏ′ = ℏκ and κ > 0.

Within the framework of some straightforward mathematical terms it is argued that there exists a space-invariant in the Schrödinger quantum mechanics (SQM). As an alternative to the geometric features of localized nature dictated by the prescribed boundary conditions in a potential problem in SQM, this spatial invariant is expected to account for some global geometric features of the quantum system.