On Amplitude Of Gauge And Gravity Theory

This thesis is mainly about amplitude in gauge and gravity theory. In the area of tree amplitude in gauge theory, the main calculating methods are CSW and BCFW method, and we use BCFW method to prove KK and BCJ relation between amplitudes. In the area of loop amplitude in gauge theory, the main method is unitarity cut method. With it, we prove some relations between1-loop amplitudes and derive some relations between2-loop amplitudes. In the area of tree amplitude in gravity theory, the direct calculations always use KLT relation, and we prove the equality between different gravity amplitude equations. In the end of this thesis, we show how to calculate cross section with spinor integration method.