Research Of Relativistic Bosons And Fermions In Non-flat Space-time

This article focuses on the spin particles in a class of curved space-time in the equations of motion and its system of conservation. Klein-Gordon equation and Dirac equation with simple forms of the universal express bosons and fermions in the field, is a powerful tool to the gravitational field of study. In the horizontal zero momentum, for the different types of curved space-time , accurate analytical form to the intrinsic wave functions of bosons and fermions have been got. The eigenvalue solutions are also divided into analytical and numerical solution methods. In this paper, analytical methods is to calculate the intrinsic equation of spin particle, a numerical study of their intrinsic value of energy. By the definition of the four-dimensional momentum operator, this paper demonstrats that ,in the non-flat space-time background, the flow probability conservation law is ture for the spin-particles. The in-depth study for the movement of particles in the curved space-time has an important significance of mathematics and physical meaning .The full text is divided into five chapters:Chapter I, Introduction. This chapter introduces the theory of spin particles on the study of the history of the progress and major achievements, and briefs the basic theories to the calculation of equations of motion to the spin-particles in a curved space-time background.Chapter II, Spin particles in the background of the curved space-time. The metric tensor of Riemann space is used to study equations of motion of the spin-particles in a curved space-time. Calculations have been used for the Klein - Gordon equation and Dirac equation through different types of curved space-time . In the calculation of the Dirac equation, we first introduced the spin about the nature of the contact with the frame field curvature tensor, and to explore the use of symbols Christofell metric scalar curvature of the particle and the geodesic equation , And the use of spin and the equivalence principle achieves Dirac equation.Chapter III, Calculation to intrinsic values of spin-particles . In a class of special boundary conditions ,We calculate the wave functions and energy intrinsic values about spin particles. In the results, The eigenvalues of bosons and fermions are compared and analyzed.Chapter IV, The particle's symmetry and conservation in curved background space-time . First of all, this chapter reviews the quantum mechanics of the law of conservation of probability flow. Then, an analysis of quantum field theory of probability flow is made. Subsequently, we make such classic conclusions into the curved space-time in order to get a more general conclusions about the particle number conservation. Finally, we also study the conservation law about the parity operator in the curved space-time .Chapter V, Summed up.