Spinors and multivectors as a unified tool for spacetime geometry and for elementary particle physics

From the definition of spinors as the minimal left (right) modules of multivectors (that is, of vectors and their outer products), we can construct a unified mathematical approach for the study of matter and its interaction fields, which are either defined as fields in the geometrical spacetime or considered as generators of the physical spacetime. It is also shown how matter and interaction fields can be represented either by spinor fields or by multivector fields, both types of fields carrying the same information as the traditional corresponding spinors, vectors, or tensors. Geometry is more transparent in one representation (multivector form), and physics is more obvious in the spinor representation. Our theory provides a unified and totally self-consistent representation of quarks (barions), leptons, and all their known interactions.     

The Casimir effect for fields with arbitrary spin

The Casimir force arises when a quantum field is confined between objects that apply boundary conditions to it. In a recent paper we used the two-spinor calculus to derive boundary conditions applicable to fields with arbitrary spin in the presence of perfectly reflecting surfaces. Here we use these general boundary conditions to investigate the Casimir force between two parallel perfectly reflecting plates for fields up to spin-2. We use the two-spinor calculus formalism to present a unified calculation of well-known results for spin-1/2 (Dirac) and spin-1 (Maxwell) fields. We then use our unified framework to derive new results for the spin-3/2 and spin-2 fields, which turn out to be the same as those for spin-1/2 and spin-1. This is part of a broader conclusion that there are only two different Casimir forces for perfectly reflecting plates—one associated with fermions and the other with bosons.     

Theory of quaternion angular momentum for unified fields of dyons

Unified quaternionic angular momentum for the fields of dyons and gravito-dyons has been developed and the commutation relations for dynamical variables are obtained in compact and consistent manner. Demonstrating the quaternion forms for unified fields of dyons (electromagnetic fields) and gravito-dyons (gravito-Heavisidian fields of linear gravity), corresponding quantum equations are reformulated in compact, simpler and manifestly covariant forms. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 14–20, December, 2006.     

A note on the geometric unification of gravity and electromagnetism

In recent years there have been many authors that have sought ageometrically unified theory of gravity and electromagnetism. It will be argued that the motivation behind the search for such a unified theory on geometric grounds alone is both erroneous and misleading. It is felt that any new unified theory of gravity and electromagnetism must include an explanation of why the existing theory is inadequate, and should provide clear physical reasons for introducing new fields (or field equations) that appear in the theory.     

电磁场统一性质的三维描述

论述了电场与磁场本质上的统一性质,构造了三维空间中电磁场的统一场量,给出它的方程、场量的模方与能量和动量的关系,发现三维空间中的统一场量自身的标积竟然是相对论变换下的不变量．     

THE U(3) ANOMALY

The U(3) anomaly will be given based upon the geometrical and topological method which was used in deterurinating the anomalies for SU(N) and SO(N) gauge fields. It is shown that both the non-Abelian and the Abelian anomaly can be derived in unified treatment from the third Chern class and corresponding Chern-Simons secondary class of the U(3) group.     

强激光场阈上电离理论

本文提出一种统一的阈上电离理论。根据该理论,可以定量描述较真实的原子阈上电离过程并能清楚地阐明实验观测的阈上电离现象。该现象可理解为前后相继的两个过程:(1)先从无场的初态吸收N个光子而到场缀末态的量子跃迁过程。(2)欲定量描述实验测量,还需考虑光电子逃离光场时与光场相互作用的“后作用效应”。该“后作用效应”是由非均匀激光场所形成的无质动力所引起的经典物理过程。 关键词：     

Generalization of Schwinger-Zwanziger Dyon to?Quaternion

Postulating the existence of magnetic monopole in electromagnetism and Heavisidian monopoles in gravitational interactions, a unified theory of gravi-electromagnetism has been developed on generalizing the Schwinger-Zwanziger formulation of dyon to quaternion in simple and consistent manner. Starting with the four Lorentz like forces on different charges, we have generalized the Schwinger-Zwanziger quantization parameters in order to obtain the angular momentum for unified fields of dyons and gravito-dyons (i.e. Gravi-electromagnetism). Taking the unified charge as quaternion, we have reformulated manifestly covariant and consistent theory for the dynamics of four charges namely electric, magnetic, gravitational and Heavisidian associated with gravi electromagnetism.     

Einheitliche Feldtheorie mit Fernparallelismus und Diracs Elektrodynamik. V (Die asymptotische Form der statischen Felder in der Einheitlichen Feldtheorie mit Fernparallelismus)

Unified Field Theory with Tele-parallelism and Dirac's Electrodynamics. V (Asymptotical Conditions for Statical Tetrads) Discussion of the asymptotical behaviour of statical tetrad fields as solutions of the generalized Einstein-Maxwell equations in the unified field theory with Einsteinian tele-parallelism. Such solutions should give stationary clouds of the classical electron-fields by Dirac.     

Gauge theories of weak and strong gravity

A review of some recent papers on gauge theories of weak and strong gravity is presented. For weak gravity, SL(2, C) gauge theory along with tetrad formulation is described which yields massless spin-2 gauge fields (quanta gravitons). Next a unified SL(2n,C) model is discussed along with Higgs fields. Its internal symmetry is SU(n). The free field solutions after symmetry breaking yield massless spin-1 (photons) and spin-2 (gravitons) gauge fields and also massive spin-1 and spin-2 bosons. The massive spin-2 gauge fields are responsible for short range superstrong gravity. Higgs-fermion interaction can lead to baryon and lepton number non-conservation. The relationship of strong gravity with other forces is also briefly considered.     

New Electroweak Model Without a Higgs Particle

A new unified electroweak model is proposed in this paper. In this unified electroweak model, Higgsmechanism is not used, so no Higgs particle exists in the model. In order to keep the masses of intermediate gaugebosons non-zero, two sets of gauge fields will be introduced. In order to introduce symmetry breaking and to help tointroduce the masses of all fields, a vacuum potential is needed. Except for those terms concerning Higgs particle, thefundamental dynamical properties of this model are similar to those of the standard model. And in a proper limit, thismodel will approximately return to the standard model. The purpose of this paper is not to say that the Higgs particledoes not exist in Nature, it is only to prove that, without a Higgs particle, we can also set up a unified electroweak modelwhich is consistent with present experiments.     

Bäcklund transformation,local and non-local conservation laws for super-chiral fields

New non-local conservation laws, parametric Bäcklund transformation and local conservation laws are constructed for super-chiral fields in general, using similar methods for ordinary chiral fields. We thus have a unified view of these field theories.     

Magnetic field in a finite toroidal domain

The magnetic field structure in a domain surrounded by a closed toroidal magnetic surface is analyzed. It is shown that ergodization of magnetic field lines is possible even in a regular field configuration (with nonvanishing toroidal component). A unified approach is used to describe magnetic fields with nested toroidal (possibly asymmetric) flux surfaces, magnetic islands, and ergodic field lines.     

THE NONABELIAN BOSONIZATION OF FERMION FIELDS IN (1+1) DIMENSIONS BY PATH INTEGRAL METHOD

Using the path integral method for handling the anomaly problem under the comoving representation,we present a unified scheme for deriving the bononization of fermion fields in (1+1) dimensions.The massless Thirring model with an external electric field,and the Gross-Neveu model with internal SU(N) symmetry,as two examples for abelian and nonabelian bosonization,are discussed repectively in some detail.     

Superconformal supergravity and internal symmetry

The Weyl-like gauging of Wess-Zumino superconformal symmetry and of its internal symmetric generalizations SU(2,2|N) are treated. The prolification of gauge fields is much more modest than in super-Riemannian theories. Unlike supergravity, a field theory of this type is still a unified theory that provides its own sources.     

Monopole and dyon solutions in SU(5) grand unified theory

Based on the method of the phase factor of the standard differential loop we obtain the general forms of static and spherically symmetric gauge potentials and Higgs fields in SU(5) grand unified theory and their ordinary differential equations. At spatial infinity and in the Higgs vacuum we obtain all the possible asymptotic behaviors of inequivalent, regular, finite-mass, static and spherically symmetric monopole and dyon solutions in SU(5) GUT.     

Unified model equations for microstructure evolution

Unified model equations hidden in microstructure evolution are discovered in this paper. The governing equations in Lifshitz-Slyozov-Wagner theory, and diffusion screening theory are derived with some approximations from the unified model equations. The governing equations in multiparticle diffusion simulation and phase-field simulation in microstructure evolution are also derived from the unified model equations. The advantages and limitations for different theories and simulations in microstructure evolution are compared in detail. This comparison can guide scientists to select computational tools for their needs in microstructure evolution. The unified model equations can be applied in many new technological fields, such as self-assembly in nanoscience.     

Monopole and topological electron dynamics in adiabatic spintronic and graphene systems

A unified theoretical treatment is presented to describe the physics of electron dynamics in semiconductor and graphene systems. Electron spin's fast alignment with the Zeeman magnetic field (physical or effective) is treated as a form of adiabatic spin evolution which necessarily generates a monopole in magnetic space. One could transform this monopole into the physical and intuitive topological magnetic fields in the useful momentum (K) or real spaces (R). The physics of electron dynamics related to spin Hall, torque, oscillations and other technologically useful spinor effects can be inferred from the topological magnetic fields in spintronic, graphene and other SU(2) systems.