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研究生:陳建和
研究生(外文):Chien-Ho Chen
論文名稱:粒子觀點下的廣義相對論
論文名稱(外文):General Relativity from the Particle''s Points of View
指導教授:高涌泉高涌泉引用關係
指導教授(外文):Yeong-Chuan Kao
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:52
中文關鍵詞:廣義相對論能量-動量張量楊-密爾斯規範理論
外文關鍵詞:energy-momentum tensorYang-Mills gauge theorygeneral relativity
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The 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 50
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