賀培銘臺灣大學：物理研究所鄭泰中Cheng, Tai-ChungTai-ChungCheng2007-11-262018-06-282007-11-262018-06-282006http://ntur.lib.ntu.edu.tw//handle/246246/54579我們簡介以正則量子化的方法處理高階微分和非侷域系統，並且證明正則量子化和路徑積分的關係。在路徑積分的計算中，期望值常常沒有簡單的時間順序。此外我們並建立了微擾的方法處理高階的波色子和費米子系統。利用此方法，不論位能形式為何，都可以將高階微分系統化為等效的低階微分系統，並得到侷限的能量形式。最後我們利用路徑積分，得到等效於開放弦的高階微分粒子的理論，並得到其對稱性和相關物理量。We review the canonical formulation for Lagrangians with higher time derivative and nonlocality of finite extent, and try to prove the relation between canonical quantization and path integral. The time-ordering is always mixed if we try to obtain the Poisson bracket for a nonlocal theory in the path integral approach. We also developed the perturbative approach to deal with Lagrangians with arbitrary higher order time derivatives for both bosons and fermions. This approach enables us to find an effective Lagrangian with only first time derivatives order by order in the coupling. The Hamiltonian is bounded from below whenever the potential is. Finally, we also got a nonlocal worldline action and consider its Virasoro algebra. It is equivalent to the worldsheet theory of a bosonic open string.Contents 1 Introduction 3 2 Canonical Quantization for Higher Derivatives 5 2.1 Lagrangians with Finite Time Derivatives 5 2.2 Lagrangians with Nonlocality of Finite Time Interval 7 2.3 Relation between Ostrogradski’s and Woodard’s Constructions 8 3 Relation between Canonical Quantization and Path Integral 10 3.1 Relation between Ostrogradski’s Formulation and Path Integral 10 3.2 Relation between Woodard’s Formulation and Path Integral 14 4 Perturbative Approach 16 4.1 First Order Approximation 17 4.2 Higher Order Approximation 18 4.3 To All Order: A Formal Proof 19 4.4 Examples 21 5 Perturbative Approach for Fermions 24 5.1 First Order Approximation 26 5.2 Higher Order Approximation 28 5.3 To All Order: A Formal Proof 29 5.4 Examples 31 6 String Lagrangian in Higher Derivative Form 35 6.1 Nonlocal action with conformal symmetry 35 6.2 Open string as nonlocal particle 39 7 Discussion 47 參考文獻 53257061 bytesapplication/pdfen-US高階微分higher time derivativethesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/54579/1/ntu-95-D89222028-1.pdf