共形Lorentz群在场论中的自然推广
A natural extension of the conformal Lorentz group in a field theory context
摘要：
本文提出了一个有限维酉结合代数，并详细讨论了它的代数自同构群。所研究的代数在物理上可以理解为在一个形式的量子场论中，对于自旋为1/2的粒子及其反粒子，在固定动量下的创造算子代数。证明了相应的自同构群的本质部分可以自然地与共形洛伦兹群相联系。此外，自同构群的非半单部分可以理解为纯单粒子态的“装扮”。所研究的数学结构可能有助于以非微扰的方式构造量子场论。此外，它提供了一个简单的例子，绕过科尔曼Mandula定理使用非半单群，没有超对称性。
英文摘要：
In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field theory at fixed momentum for a spin 1/2 particle along with its antiparticle. It is shown that the essential part of the corresponding automorphism group can naturally be related to the conformal Lorentz group. In addition, the non-semisimple part of the automorphism group can be understood as "dressing" of the pure one-particle states. The studied mathematical structure may help in constructing quantum field theories in a non-perturbative manner. In addition, it provides a simple example of circumventing Coleman-Mandula theorem using non-semisimple groups, without SUSY.
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