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  • 學位論文

紫外收斂量子場論

A UV finite quantum field theory

指導教授 : 賀培銘

摘要


在先前的成果中,一個圈圖收斂的φ4 理論被成功建構。在這本論文中,第一部份將把前述的結果推廣到在任意偶數維度的任意純量場交互作用φn理論皆適用。這一部份亦發表在賀培銘教授與我合作的期刊論文中。 在這本論文的第二部份,將探討自旋一向量場之推廣。一個圈圖收斂的電磁交互作用被成功建立。文末將探討推廣至自旋一非阿貝爾群交互作用的場論以及進一步推廣至自旋二之重力交互作用甚至高階自旋理論之可行性。

並列摘要


In previous works1, a UV-finite φ4 theory is successfully established. In the first part of this thesis, we generalize this result to arbitrary φn theories in arbitrary even dimensions. This part is also published in the journal JHEP2. In the second part, we further generalize this framework to spin-one fields. In the end we discuss the future direction of generalization to non-abelian gauge theories and gravity theory.

參考文獻


[1] Pei-Ming Ho and Yi-Ya Tian, UV-finite scalar field theory with unitarity, [hep- th/0410248v2]
[3] R.P. Feynman, Space-Time Approach To Quantum Electrodynamics," Phys. Rev. 76. 769(1949)
[4] Pauli, W., Villars, F. On the Invariant Regularization in Relativistic Quantum Theory, Rev. Mod. Phys, 21, 434-444 (1949)
[5] R.E. Cutkosky, Singularities And Discontinuities Of Feynman Amplitudes," J. Math. Phys. 1, 429 (1960)
[6] Aitchison, I.J.R. , Hey, A.J.G.(1982), Gauge Theories in Particle Physics, Adam Hilger.

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