高涌泉臺灣大學：物理研究所郭婉如Wan-Jung, KuoKuoWan-Jung2007-11-262018-06-282007-11-262018-06-282004http://ntur.lib.ntu.edu.tw//handle/246246/54512Historically, general relativity originates from a geometrical viewpoint, i.e., gravity is regarded as the curvature of the spacetime. However, thanks to the invention of quantum field theory, there exists another viewpoint which treats gravity effect as an exchange of massless spin 2 gravitons between particles. Formulating the theory of general relativity makes it possible that the ultimate laws of nature can be formulated in a united, universal framework and that gravity should be promoted to a quantized theory. In the first part of this thesis, we develop the theory of a free graviton and will find an inconsistency in our theory should be solved. We focus on Feynman’s and Deser’s approaches to the problem, clarifying the meaning of their methods and explicitly working out the calculations to see if their results are correct. Field theory formulated in a noncommutative space is expected to possess a property called UV/IR mixing originated from the nonlocal property of product of functions on noncommutative space. Hence, due to this nontrivial mixture between UV and IR phenomena in noncommutative quantum field theory, we expect that when considering NC-QFT at finite temperature, the chiral anomaly will have temperature dependence. In the second part of this thesis, we explicitly carry out the one-loop calculation of chiral anomaly in (1+1)-dim NC-QED at finite temperature in this thesis to see whether that expectation is true.Contents General Relativity as a Self-consistent theory of Spin-2 Particles Chapter 1 Introduction 7 Chapter 2 Feynman’s Approach 10 2.1 Feynman’s Strategy 10 2.2 The meaning of 12 2.3 13 2.4 Reexamination 14 2.5 Expanding Einstein’s Lagrangian 18 2.6 Comparison with Feynman’s result 20 Chapter 3 Deser’s Approach 22 3.1 The first order formalism 22 3.2 The consistency of pure gravity 24 3.2.1 The iterative procedure 25 3.2.2 The convenient variable, tensor density 26 3.2.3 t' 27 3.2.4 The complete Lagrangian for pure gravity 29 3.2.5 Consistency of complete Lagrangian 30 3.3 Interaction with matter 32 3.4 Comments 33 Chapter 4. Conclusions 36 Appendix 1 The missing steps of the calculation of 38 A1.1 The remaining 14 possible terms written by independent terms 38 A1.2 The calculations of sym 39 Appendix 2 The cubic terms in Einstein’s Lagrangian 42 Appendix 3 Expanding Einstein’s equation 48 A3.1 The linear part of Einstein’s equation 48 A3.2 Weinberg’s t 49 Appendix 4. First order formalism 52 A4.1 The field equation of free gravitons 52 A4.2 The field equation for pure gravity 54 Bibliography 57 The temperature effect of chiral anomaly in (1+1)-D NC-QED Chapter 1. Introduction 59 Chapter 2. QED on a noncommutative space 60 2.1 The algebra of noncommutative geometry 60 2.2 NC-QED 63 2.2.1 Feynman rules 63 2.2.2 Symmetries and currents 64 Chapter 3. Finite temperature field theory 66 3.1 Imaginary time formalism 66 3.2 Real time formalism 67 Chapter 4. The temperature effect of chiral anomaly in (1+1)-D NC-QED 69 4.1 Feynman rules of NC-QED at finite temperature 69 4.2 Point splitting regularization 70 4.3 Dimensional regularization 73 4.3.1 J' 74 4.3.2 J 78 4.3.3 Photon loop 79 Chapter 5. Conclusions 81 Appendix A 83 Bibliography 872715362 bytesapplication/pdfen-US重力非交換場論NC-QEDspin-2gravityEinsteinnoncommutative field theorychiral anomalythesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/54512/1/ntu-93-R91222005-1.pdf