International Journal of Modern Physics A

We review the construction and classification of three-family grand unified models within the framework of asymmetric orbifolds in perturbative heterotic superstring. We give a detailed survey of all such models which is organized to aid analysis of their phenomenological properties. We compute tree level superpotentials for these models. These superpotentials are used to analyze the issues of proton stability (doublet–triplet splitting and R-parity-violating terms) and Yukawa mass matrices. To have agreement with phenomenological data all these models seem to require a certain degree of fine-tuning. We also analyze the possible patterns of supersymmetry breaking in these models. We find that the supersymmetry breaking scale comes out either too high to explain the electroweak hierarchy problem, or below the electroweak scale unless some degree of fine-tuning is involved. Thus, none of the models at hand seem to be phenomenologically flawless.

We discuss the recent model of a Quantum Mechanical Black Hole (QMBH) which describes the most fundamental known particles, the leptons and approximately the quarks in terms of the Kerr–Newman Black Hole with a naked singularity shielded by Zitterbewegung effects. This goes beyond the Zitterbewegung and self interaction models of Barut and Bracken, Hestenes, Chacko and others and provides a unified picture which amongst other things gives a rationale for and an insight into:

(1) The apparently inexplicable reason why complex space–time transformations lead to the Kerr–Newman metric in General Relativity.

(2) The value of the fine structure constant.

(3) The ratio between electromagnetic and gravitational interaction strengths.

(4) The anomalous gyromagnetic ratio for the electron.

(5) Why the neutrino is left-handed.

(6) Why the charge is discrete.

In the spirit of Effective Field Theories, this model provides an alternative formalism for Quantum Theory and also for its combination with General Relativity.

Finally a mechanism for the formation of these QMBH or particles is explored within the framework of Stochastic Electrodynamics, QED and Quantum Statistical Mechanics. The cosmological implications are then examined. It turns out that a surprisingly large number of facts, including some which were hitherto inexplicable. follow as a consequence of the model. These include a theoretical deduction of the Mass, Radius and Age of the Universe, also the values of Hubble's constant and the Cosmological constant.

We present here an accurate exponentially fitted explicit four-step method for the numerical integration of the one-dimensional Schrödinger equation. The formula considered contains free parameters which are defined in order to integrate exponential functions. We note that this is the first explicit four-step exponentially fitted method in the literature. Numerical results also indicate that the new method is much more accurate than other well-known methods.

We formulate the flipped SU(5)×U(1)-GUT within a Lie-algebraic approach to non-commutative geometry. It suffices to take the matrix Lie algebra su(5) as the input; the u(1)-part with its representation on the fermions is an algebraic consequence. The occurring Higgs multiplets (24, 5, 45, 50-representations of su(5)) are uniquely determined by the fermionic mass matrix and the spontaneous symmetry breaking pattern to SU(3)_C×U(1)_EM. We find the most general gauge invariant Higgs potential that is compatible with the given Higgs vacuum. Our formalism yields tree-level predictions for the masses of all gauge and Higgs bosons. It turns out that the low-energy sector is identical with the standard model. In particular, there exists precisely one light Higgs field, whose upper bound for the mass is 1.45 m_t. All remaining 207 Higgs fields are extremely heavy.

For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical space–time, at least approximately. However, quantum gravity may eventually provide classical space–times by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a space–time manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach.

Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of histories.