高涌泉臺灣大學：物理研究所陳建和Chen, Chien-HoChien-HoChen2007-11-262018-06-282007-11-262018-06-282004http://ntur.lib.ntu.edu.tw//handle/246246/54651The concept of the gravitational field energy-momentum tensor is an interesting problem from the time of Einstein's general relativity established. It allures a lot of the theoretical and experimental physicsts to discuss and dispute it. The thesis is presented in a self-contained manner. We gives a review of the some topics about the gravitational theory including the preliminary of the spin 2 graviton and the canonical and metric energy-momentum tensors of the diverse fields. We derive the Yang-Mills gauge theory of the first-order and second-order formalisms by requiring minimal-coupling and gauge invariant. The Einstein gravitational theory in the first-order form is derived from the the linear theory, but for the second-order form we need to do infinite times of iterations. Finally, different definitons of the graviton energy-momentum tensor density is considered. We show that they are not equal since we can choose an inertial coordinate frame to eliminant the effect of gravity by the equivalence principle. Consequently, the local energy-momentum tensor is meaningless.1 Introduction and Some Background Knowledge 3 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Weak Field Approximation andGraviton . . . . . . . . . . . . 4 1.3 Energy-MomentumTensor in the Field Theory . . . . . . . . . 9 1.4 Tensor Density, Metric Density and Metric Determinant . . . 13 2 Yang-Mills Gauge Theory 15 2.1 Gell-Mann-Levy Equation . . . . . . . . . . . . . . . . . . . . 15 2.2 Derivation of Yang-Mills Lagrangian and Equation . . . . . . 18 2.2.1 The First -Order Formalism . . . . . . . . . . . . . . . 18 2.2.2 The Second-Order Formalism . . . . . . . . . . . . . . 20 3 Field Theoretic Approach to the Gravitational Theory 24 3.1 Derivation of the Field Equation of the General Relativity . . 24 3.2 Derivation of the Linearized Einstein Equation . . . . . . . . . 25 3.3 Derivation the Full Einstein-Hilbert Action . . . . . . . . . . . 28 4 Three-Graviton Interaction Lagrangian Density 32 4.1 Three-Graviton Interaction and the Energy-Momentum Tensor fromthe LagrangianDensity . . . . . . . . . . . . . . . . . 32 4.2 Energy-Momentum Tensor Density from the Einstein Tensor . 35 4.3 Conservation Law of the Total Energy-Momentum Density . . 38 4.4 Conservation Laws of the Energy-MomentumTensor . . . . . 40 4.5 Gupta and Feynman’s Procedure . . . . . . . . . . . . . . . . 40 5 Conclusions 46 A Auxiliary Metric Tensor 47 B Three-Graviton Interaction Lagrangian Density 48 C Notations and Conventions 50312984 bytesapplication/pdfen-US廣義相對論能量-動量張量楊-密爾斯規範理論energy-momentum tensorYang-Mills gauge theorygeneral relativitythesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/54651/1/ntu-93-R89222035-1.pdf