Unitarity of Higher Derivative Field Theories

本論文是研究再平坦時空高次微分量子場論的微擾么正性.我們將會討論建構一個同時具么正性以及紫外有限場論的困難.This thesis is devoted to the study of the perturbative unitarity of higher derivative quantum field theories in n-dimensional flat spacetime. The difficulties associated with formulating a consistent UV finite and unitary quantum field theory are explained.ch1 Introduction ........................................1 1.1 Introduction.........................................1 ch2 Higher Derivative Theories...........................5 2.1 Two Coupled Springs..............................5 2.2 Space-Time Noncommutative Field Theories.........8 ch3 Scattering Matrix...................................12 3.1 The S-matrix....................................12 3.2 Causality.......................................13 3.3 Formulation of the S-Matrix.....................16 3.3.1 Relativistic Covariance and Unitarity of the S-Matrix..............................16 3.3.2 The conditionof Causality.................18 3.3.3 Expansion of the S-Matrix.................21 3.3.4 Conditions of Covariance, Unitarity, and Causality for S_n.........................21 3.3.5 Explicit form of S_1 and S_2..............24 3.4 Unitarity.......................................28 3.5 Hermitian Analyticity...........................30 3.6 Proof in Perturbation Theory....................34 ch4 Unitarity of Higher Derivative Field Theory.........39 4.1 Introduction....................................39 4.2 Something about the Propagator..................41 4.3 Phi-4 theory....................................45 4.3.1 UV_divergence.............................46 4.3.2 Perturbative Unitarity....................51 4.3.3 Generic Feynman diagrams..................52 4.4 Regularization by analytic continuation.........54 4.4.1 The operator..............................55 4.4.2 One-loop diagrams.........................56 4.4.3 Generic one-loop diagrams.................59 ch5 Discussion..........................................61 5.1 More about the propagator.......................61 5.2 Comments on unitarity...........................62 5.3 Generalizations.................................63 References..............................................6