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arXiv 0904.1398nucl-th
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Kadyshevsky公式中的π-核子散射和高自旋场量子化

Pion-Nucleon Scattering in Kadyshevsky Formalism and Higher Spin Field Quantization

J. W. Wagenaar

摘要:

本文分为两个部分。第一部分讨论Kadyshevsky形式中的π-核子/介子-重子散射。这种形式主义的介绍和讨论。当使用导数耦合和/或更高的自旋场时,可能会出现问题,特别是当与费曼形式主义的结果相比时:不需要的接触项弹出。这些条款使用Gross和Jackiw或Takahashi和Umezawa方法取消。因此,两种形式主义的最终结果是相等的、因果的和协变的。正式纳入对抑制重子交换部门实现使用的方法的基础上的高桥和梅泽方法。对于由此产生的树级振幅,我们已经表明,我们的知识的第一次,他们是因果关系,协变和n-独立的。此外,振幅只是通常费曼表达式的1/2倍。振幅只包含正能量的初始和最终状态,尽管应该提到的是,负能量通过Delta传播子存在于振幅内。本文的第二部分在狄拉克约束分析的框架下研究了高自旋场的量子化。对自由自旋为1、3/2和2的情况以及这些场与辅助场耦合的情况给出了一个完整的约束分析和量子化过程。在前一种情况下构造的传播子被证明是非协变的,这是众所周知的。因此,辅助场耦合到规范条件的自由情况下引入的拉格朗日。现在,得到的传播子是协变的。

英文摘要:

This thesis contains two parts. The first part deals with pion-nucleon/meson-baryon scattering in the Kadyshevsky formalism. This formalism is introduced and discussed. Problems may arise when derivative couplings and/or higher spin fields are used, especially when compared to the results in the Feynman formalism: unwanted contact terms pop-up. These terms are cancelled using the Gross and Jackiw or Takahashi and Umezawa method. The final results in both formalisms are therefore equal, causal and covariant. Formal incorporation of pair suppression in the baryon exchange sector is achieved using a method based on the Takahashi and Umezawa method. For the resulting tree level amplitudes, we have shown, to our knowledge for the first time, that they are causal, covariant and n-independent. Moreover, the amplitudes are just a factor 1/2 of the usual Feynman expressions. The amplitudes contain only posititve energy initial and final states, although it should be mentioned that negative energy is present inside an amplitude via the Delta propagator. The second part of this thesis deals with higher spin field quantization in the framework of Dirac's Constraint analysis. A full constraint analysis and quantization procedure is presented for the free spin 1,3/2 and 2 case and for the situation where these fields are coupled to auxiliary fields. The constructed propagators in the former case are shown to be non-covariant, as is well-known. Therefore, auxiliary fields coupled to gauge conditions of the free case are introduced in the Lagrangian. Now, the resulting propagators are covariant.

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