Restatement and Extension of Various Spin Particle Equations

This paper is based on my own previous articles. I improve research methods and add some new contents in this paper. A more rigorous, more analytical, more complete and more organized mathematical physical method is adopted. And I am as far as possible to make the whole article have a sense of beauty. Firstly, the mathematics foundation of constant tensors analysis methods is established rigorously in Chapter One. Some wonderful mathematical properties are found. Many important constant tensors are proposed. Then in Chapter Two I use constant tensors as a mathematical tool to apply to physics. Some important physical quantities are defined by using constant tensors. All kinds of relationships between them are studied in detail. The canonical, analytical and strict mathematical physical sign system is established in this chapter. In Chapter Three, I use the mathematical tools in the previous two chapters to study spinorial formalism of various spin particles classical equations. And the equivalence between spinorial formalism and classical one is proved strictly. I focuse to study electromagnetic field, Yang-Mills field and gravitational field etc. Especially, a new spinorial formalism of the gravitational field identity is proposed. In order to further explore, I study several important equations by contrast. Some new and interesting results are obtained. The Chapter Four is the most important part of this thesis. It is also my original intention of writing this paper. In this chapter, I put forward a new form of particle equations: Spin Equation. The equation is directly constructed by spin and spin tensor. And I note that spin tensor is also the transformation matrix of corresponding field representation. So the physical meaning of this equation is very clear. The corresponding particle equation can be simply and directly written according to the transformation law of the particle field. It correctly describes neutrino, electromagnetic field, Yang-Mills field and electron etc. And it is found that it is completely equivalent to full symmetry Penrose equation. A scalar field can be introduced naturally in this formalism. Thus, a more interesting equation is obtained: Switch Spin Equation. When the scalar field is zero, free particles can exist. When the scalar field is not zero, free particles can't exist. The scalar field acts as a switch. It can control particles generation and annihilation. This provides a new physical mechanism of particles generation and annihilation. At the same time, it can also answer the question: why the universe inflation period can be completely described by the scalar fields. And the equation itself has an inherent limitation to the scalar field. So that the scalar will be quantized automatically. Each quantized value of the scalar is corresponding to different physical equations. That provides a new idea and an enlightenment for unity of five superstring theories. Finally, in Chapter Five Bargmann-Wigner equation is analyzed thoroughly. It is proved that it is equivalent to Rarita-Schwinger equation in half integer spin case. And it is equivalent to Klein-Gordon equation in integer spin case. The profound physical meanings of Bargmann-Wigner equation are revealed. By contrast, it is found that Bargmann-Wigner equation is suitable to describe massive particles, but not too suitable to describe massless particles. Penrose spinorial equation or Spin Equation is more suitable to describe massless particles. Mathematics and physics of this paper have a stronger originality. Some mathematical and physical concepts, methods and contents also have a certain novelty. All of them are strictly calculated and established step by step by my own independent efforts. It takes me a lot of time and energy. I use spare time to finish the paper. Due to the limited time and my limited level, it is inevitable that there are a few mistakes. Comments and suggestions are welcome!