打开量子旋量场的潘多拉盒子
Opening the Pandora's box of quantum spinor fields
摘要：
Lounesto的旋量分类是一个全面和详尽的算法，基于双线性协变，揭示了各种旋量的可能性，包括正则和奇异旋量及其在物理学中的意想不到的应用，包括Dirac，Weyl和Majorana作为非常特殊的旋量场。在本文中，我们提出了一个类似的分类问题的框架内的第二量化。我们首先一般地讨论问题的性质。然后，我们开始分析两个基本的双线性协变量，标量和赝标量，在第二个量子化的设置，适用于量子场论的表达式扩展到所有类型的旋量。人们可以看到，相对于经典情况，一组更广泛的可能性打开了大门。提出了一种量子重建算法。Feynman传播子被推广到所有类的旋量。
英文摘要：
Lounesto's classification of spinors is a comprehensive and exhaustive algorithm that, based on the bilinears covariants, discloses the possibility of a large variety of spinors, comprising regular and singular spinors and their unexpected applications in physics and including the cases of Dirac, Weyl, and Majorana as very particular spinor fields. In this paper we pose the problem of an analogous classification in the framework of second quantization. We first discuss in general the nature of the problem. Then we start the analysis of two basic bilinear covariants, the scalar and pseudoscalar, in the second quantized setup, with expressions applicable to the quantum field theory extended to all types of spinors. One can see that an ampler set of possibilities opens up with respect to the classical case. A quantum reconstruction algorithm is also proposed. The Feynman propagator is extended for spinors in all classes.
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