高階微分理論

On Higher Time Derivative Theory

鄭泰中(Tai-Chung Cheng)

指導教授 ： 賀培銘

國立臺灣大學/理學院/物理研究所/博士(2006年)

https://doi.org/10.6342/NTU.2006.01041

摘要

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。

關鍵字

高階微分

並列摘要

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.

並列關鍵字

higher time derivative

參考文獻

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