Private monochromatic solutions of the free-field equation of electro-gravimagnetic charges and currents are constructed in the differential algebra of biquaternions, which describe elementary particles as standing el...Private monochromatic solutions of the free-field equation of electro-gravimagnetic charges and currents are constructed in the differential algebra of biquaternions, which describe elementary particles as standing electro-gravimagnetic waves. The two classes of solutions of this biquaternionic wave equation have been investigated, generated by scalar potentials (pulsars) and vectorial potentials (spinors). Their asymptotic properties are considered, on the base of which they are classified into heavy (boson) and light (lepton) elementary particles. The biquaternion representation of the hydrogen atom is given. The periodic system of elements is produced, which is built on the principle of the musical structure of a simple gamma.展开更多
One the base of differential algebra of biquaternions, the one model of electro-gravimagnetic interactions of electric and gravimagnetic charges and currents has been constructed. For this, three Newton laws analogues...One the base of differential algebra of biquaternions, the one model of electro-gravimagnetic interactions of electric and gravimagnetic charges and currents has been constructed. For this, three Newton laws analogues are used. The closed system of biquaternionic wave equations is constructed for determination of the charges-currents and electro-gravimagnetic fields and united field of interactions. The equation of charge-current transformation is like the generalization of biquaternionic presentation of Dirac equation. The properties of its solutions are described, depending on properties of external EGM field. The biquaternions of energy-pulse of EGM-field and charges-currents are considered. The energy-pulse of EGM-interactions is calculated.展开更多
One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free...One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free system of electric and gravimagnetic charges and currents and generated by them EGM-field. By using generalized functions theory the fundamental and regular solutions of this system are determined and some of them are considered (spinors, plane waves, shock EGM-waves and others). The properties of these solutions are investigated.展开更多
On the base of differential biquatemions algebra and theories of generalized functions the biquaternionic wave equation of general type is considered under vector representation of its structural coefficient. Its gene...On the base of differential biquatemions algebra and theories of generalized functions the biquaternionic wave equation of general type is considered under vector representation of its structural coefficient. Its generalized decisions in the space of tempered generalized functions are constructed. The elementary twistors and twistor fields are built and their properties are investigated. Introduction. The proposed by V.P. Hamilton quatemions algebra [1] and its complex extension - biquaternions algebra are very convenient mathematical tool for the description of many physical processes. At presence these algebras have been actively used in in the work of various authors to solve a number of problems in electrodynamics, quantum mechanics, solid mechanics and field theory. The properties of these algebras are actively studied in the framework of the theory of Clifford algebras. In the papers [2, 3] the differential algebra of biquatemions has been elaborated for construction of generalized solutions of the biquaternionic wave （biwave） equations. The particular types of biwave equations were considered, which are equivalent to the systems of Maxwell and Dirac equations and their generalizations, their biquaternionic decisions also were constructed. Here the biwave equation is considered with vector structural coefficient which is biquaternionic generalization of Dirac equations. Their generalized solutions in the space of tempered distributions are defined and their properties are researched.展开更多
文摘Private monochromatic solutions of the free-field equation of electro-gravimagnetic charges and currents are constructed in the differential algebra of biquaternions, which describe elementary particles as standing electro-gravimagnetic waves. The two classes of solutions of this biquaternionic wave equation have been investigated, generated by scalar potentials (pulsars) and vectorial potentials (spinors). Their asymptotic properties are considered, on the base of which they are classified into heavy (boson) and light (lepton) elementary particles. The biquaternion representation of the hydrogen atom is given. The periodic system of elements is produced, which is built on the principle of the musical structure of a simple gamma.
文摘One the base of differential algebra of biquaternions, the one model of electro-gravimagnetic interactions of electric and gravimagnetic charges and currents has been constructed. For this, three Newton laws analogues are used. The closed system of biquaternionic wave equations is constructed for determination of the charges-currents and electro-gravimagnetic fields and united field of interactions. The equation of charge-current transformation is like the generalization of biquaternionic presentation of Dirac equation. The properties of its solutions are described, depending on properties of external EGM field. The biquaternions of energy-pulse of EGM-field and charges-currents are considered. The energy-pulse of EGM-interactions is calculated.
文摘One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free system of electric and gravimagnetic charges and currents and generated by them EGM-field. By using generalized functions theory the fundamental and regular solutions of this system are determined and some of them are considered (spinors, plane waves, shock EGM-waves and others). The properties of these solutions are investigated.
文摘On the base of differential biquatemions algebra and theories of generalized functions the biquaternionic wave equation of general type is considered under vector representation of its structural coefficient. Its generalized decisions in the space of tempered generalized functions are constructed. The elementary twistors and twistor fields are built and their properties are investigated. Introduction. The proposed by V.P. Hamilton quatemions algebra [1] and its complex extension - biquaternions algebra are very convenient mathematical tool for the description of many physical processes. At presence these algebras have been actively used in in the work of various authors to solve a number of problems in electrodynamics, quantum mechanics, solid mechanics and field theory. The properties of these algebras are actively studied in the framework of the theory of Clifford algebras. In the papers [2, 3] the differential algebra of biquatemions has been elaborated for construction of generalized solutions of the biquaternionic wave （biwave） equations. The particular types of biwave equations were considered, which are equivalent to the systems of Maxwell and Dirac equations and their generalizations, their biquaternionic decisions also were constructed. Here the biwave equation is considered with vector structural coefficient which is biquaternionic generalization of Dirac equations. Their generalized solutions in the space of tempered distributions are defined and their properties are researched.
