The Amplitude Relations In The Perturbative String Theory

In this thesis, we mainly study several problems on the String perturbation theory, which contains Kawai-Lewellen-Tye (KLT) relation between open and closed string tree amplitudes, equivalent monodromy relations for open string am-plitudes, primary relations and explicit minimal-basis expansion for open string color-ordered tree amplitudes, the relationship between resonance limit and col-or dual form for amplitudes, and monodromy relations for 1-loop open string amplitudes.The connections between KLT relation and Wick rotation is discussed. The KLT relation is proved in new way without the deformations of contour integral and the important links among ultraviolet cut, time ordered product and KLT relation has been shown.The relations between open string color-ordered tree amplitudes has been studied. Equivalent monodromy relations, including KK-BCJ relations, general-ized KK-BCJ relations and generalized U(1)-like decoupling, for open string am-plitudes is given. Primary relations-fundamental BCJ relation as well as cyclic relation, and explicit minimal-basis expansion for open string color-ordered tree amplitudes is given.monodromy relations and its' low-energy limit for 1-loop open string ampli-tudes is investigated.The structure of open and closed string tree amplitudes is studied from the standpoint of resonance limit and color dual form for amplitudes. The new new color decompositions for open string amplitudes at tree level, BCJ relations near the resonance limit, and duality between world sheet singularity and momentum pole are given. Jacobi's identity and color dual form for string amplitudes is studied.