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Clifford algebra, Lorentz transformation and unified field theory. (English) Zbl 1396.83013

Summary: According to a framework based on Clifford algebra \(C\ell (1,3)\), this paper gives a classification for elementary fields, and then derives their dynamical equations and transformation laws in detail. These results provide an outline on elementary fields and some new insights into their unusual properties. All elementary fields exist in pairs, and one part of the pair is a complex field. Some intrinsic symmetries and constraints such as Lorentz gauge condition are automatically included in the canonical equation. Clifford algebra \(C\ell (1,3)\) is a natural language to describe the world. In this language, the representation formalism of dynamical equation is symmetrical and elegant with no more or less contents. This paper is also a summary of some previous problem-oriented researches. Solutions to some simple equations are given.

MSC:

83C47 Methods of quantum field theory in general relativity and gravitational theory
15A66 Clifford algebras, spinors
53Z05 Applications of differential geometry to physics
83A05 Special relativity
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
81V22 Unified quantum theories
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