The Odd SO(3,3) Fusions and the Gauge Principle

The origin of the gauge principle generating electroweak and gravistrong interactions is shown to lie already in the quaternionic vacuum. The leptonic Dirac equations gauged in respect of the electroweak and the linearized gravistrong field are derived from the SO(3,3) fusion 6 × 4 = 20 + 4 as a part of 4 × 4 × 4 . The procedure leading to respective equations including self-interactions and gauge coupling to the full nonlinear gravistrong field via 20 ″ × 4 = 60 + 20 as a part of 4 × 4 × 4 × 4 × 4 is outlined.     

The SO(3,3) group as a common basis for Dirac's and Proca's equations

Dirac's and Proca's equations are unified in the sense that the algebras of Dirac -matrices and Duffin-Kemmer-matrices are shown to furnish two distinct matrix representations of the Lie algebra of the SO(3,3)-group. This fact is then interpreted as evidence for the classical picture of particles described by the above-mentioned equations to be a relativistic top. It is also argued that the shape of the top is rod-like.     

Electrodynamics in terms of functions over the groupSU(2): II. Quantization

In a previous article by two of the present authors Carmeli's group-theoretic method for the formulation of wave equations was applied to the case of the electromagnetic field, and the equations for the vector potential were derived. In the present paper a quantization procedure for these equations is carried out in the Lorentz gauge. It involves two independent variables, corresponding to the number of degrees of freedom of the electromagnetic field in a Hilbert space with a positive-definite metric. Conserved quantities are derived.     

A unified treatment of the groups SO(4) and SO(3,1)

The irreducible representations of the group SO(4) in which the SO(3) subgroup is reduced are studied by an explicit construction of the operators and the basis in the spinor representation. The basis function which is formally identical with that for the coupling of two angular momentaj ₁ andj ₂ is expressible in terms of a hypergeometric function and strongly resembles the one for the irreducible representations of the groups SO(3,1). For the Lorentz group, the bases for the unitary representations which require unphysical values ofj ₁ andj ₂ are found to be analytic continuation of those for SO(4). The realization of the unitary irreducible representations of the group SO(4) in the Hilbert space of these functions leads, for appropriate unphysical values ofj ₁,j ₂, to the Gelfand-Naimark formula for the principal and complementary series of the representations of SO(3;1). The matrix elements for finite transformations of SO(4) and SO(3,1) can be evaluated, in this approach, in a unified manner by using standard properties of the hypergeometric function. These turn out to be a finite sum of₃ F ₂-functions which, as expected, are polynomials for SO(4) and infinite series for SO(3,1). A number of special matrix elements are calculated from the general formula and these agree with the results obtained previously.The authors are deeply indebted to Professor S.Dutta Majumdar fo many important suggestions and clarifications.     

Preons and SO(10)

Two composite models based on SO(10) are explored, the first containing a fermion and a scalar each in the 16 rep, the second containing two fermion reps 10 + 16. The second model contains a massless composite fermion in the confined picture with a Higgs picture interpretation.     

时空对称性与守恒律(下篇)——经典电动力学

本文从时空对称性导出经典电动力学中能量、动量、角动量三大守恒定律.     

On Some Processes of Quantum Gravitation (Radiative Corrections)

Within the framework of the quantum theory of interactions of nonpoint (smeared out) particles [1], the radiative corrections due to gravitational interactions are examined. The gravitational masses are calculated for a photon, a graviton, and some other particles together with the renormalized gravitational interaction constant K(m) depending on the interacting particle mass m. The approximate character of the equivalence principle is confirmed.     

Flipped SO(10)

We constract an N = 1 supersymmetric SO(10) GUT broken down to SU(3)_c×SU(2)_L×U(1)_Y with an intermediate flipped SU(5)×U(1)_X gauge symmetry. A solution to the triplet-doublet mass-splitting problem is proposed in terms of a non-minimal missing-partner mechanism.     

The Rotational Spectrum of SO(2) and the Determination of the Hyperfine Constants and Nuclear Magnetic Shielding Tensors of (33)SO(2) and SO(17)O

Rotational analyses of the B(2)Sigma(+)(u) --> X(2)Sigma(+)(g) system of the (14)N(+)(2) molecule have been extended to include the vibrational levels up to v' = 4. Spectral data from 20 bands obtained from high-resolution Fourier transform spectrometry of a hollow-cathode and a Pointolite lamp were included in the analysis. A global deperturbation yielded molecular parameters of the highly perturbed B(2)Sigma state and interaction parameters A(2)Pi(u) approximately B(2)Sigma(u) with a standard deviation of 0.011 cm(-1). Rotational term values of the B(2)Sigma(+) state were also determined. New perturbations in the B(2)Sigma(+) (v = 0) level have been observed at N approximately 85 and N approximately 96. Copyright 2000 Academic Press.     

SO(10) v ×SO(10) H grand unified-extended technicolour models

We discuss a recently proposedSO(10) _v ×SO(10) _H grand unified-extended technicolour model. Because proton decay is probably too fast in this model, we study the other possible models based onSO(10) _v ×SO(10) _H . As a result of this analysis only a few of these models could possibly be realistic, they would be slight modifications of that previously proposed. None of them predicts the expected value forΛ _TC, it must be adjusted by introducing another mass scale. In these models ordinary fermion masses tend to be too small.     

Fractional Quantum Hall Effect and (2 + 1)-Dimensional Quantum Electrodynamics

By investigating the gap equation defining thefull electron propagator in the framework of (2 +1)-dimensional quantum electrodynamics, we derive thefractional quantum Hall effect at the filling factors = 1/2, 1/3, 2/5, 1/9. In particular, thevalue = 1/2 emerges as the lowest order of thedevelopment of this gap equation.     

On the SO(7) symmetry of the SO(8) monopole and quadrupole pairing model

The SO(7) D-pairing symmetry of the SO(8) monopole and quadrupole pairing model is shown to be unusual in that there is no corresponding group generated only by number-conserving operators. Rather, the SO(7) symmetry is manifested in terms of number-conserving operators only by taking a particular combination of the Casimir operators appropriate for the other subgroup chains.     

On (3,3)-Homogeneous Greechie Orthomodular Posets

We describe (3,3)-homogeneous orthomodular posets for some cardinality of their sets of atoms. We examine a state space and a set of two-valued states of such logics. Particular homogeneous OMPs with exactly k pure states (k = 1,...,7, 10,11) have been constructed.     

Gravitation and electromagnetism

We obtain a general relativistic unification of gravitation and electromagnetism by simply(1) restricting the metric so that it admits an orthonormal tetrad representation in which the spacelike vectors are curl-free, and(2) identifying the timelike vector as the potential for an electromagnetic field whose only sources are singularities. It follows that: (A) The energy density is everywhere nonnegative, (B) the space is flat if and only if the electromagnetic field vanishes, (C) the vector potential (through which all curvature enters) admits no invariant algebraic decomposition, and satisfies the covariant Lorentz condition identically, (D) the theory is free of prior geometry, (E) the electromagnetic self-energy of a spherically symmetric point charge equalsMC ² , (F) particles deviate from geodesic motion according to the Lorentz force law with radiative reaction, and (G) particles with all electromagnetic multipole structures are included.     

Nuclear Algebraic Geometry and SO(10)

In this contribution nuclear representations of the Dirac ring, developed over many years, are shown to be a particular case of a theorem in algebraic geometry which at the same time associates them with a Hodge decomposition of a Kaehler manifold. This yields a shape that in some cases is independent of any appeal to a symmetry group. However, because the nuclear representations are in the infinitesimal ring of SO(4) and the internal space of each representation is in a Kaehler (even Calabi-Yau) manifold K; the group SO(10) = SO(4) × K can give additional information. This paper develops the very fruitful symbiosis between algebra and irreducible representations of SO(10) and covers some aspects of string theory.     

Explanation of the Motionless Electromagnetic Generator with O(3) Electrodynamics

Recently, Bearden el al. developed a device which is known as a motionless electromagnetic generator (MEG) and which produces a coefficient of performance (COP) far in excess of unity. The device has been independently replicated by Naudin. In this communication, the fundamental operational principle of the MEG is explained using a version of higher symmetry electrodynamics known as O(3) electrodynamics, which is based on the empirical existence of two circular polarization states of electromagnetic radiation, and which has been developed extensively in the literature. The theoretical explanation of the MEG with O(3) electrodynamics is straightforward: Magnetic energy is taken directly ex vacua and used to replenish the permanent magnets of the MEG device, which therefore produces a source of energy that, in theory, can be replenished indefinitely from the vacuum. Such a result is incomprehensible in U(1) Maxwell-Heaviside electrodynamics.