标题： 高自旋Clifford分析中的玻色拉普拉斯算子 显示英文标题

标题： Bosonic Laplacians in higher spin Clifford analysis

摘要： 在本文中，我们首先介绍高自旋Clifford分析，它们是通过考虑取值于自旋群不可约表示的函数而对经典Clifford分析的推广。 然后，我们在高自旋Clifford分析中引入了一类二阶共形不变微分算子，称为玻色拉普拉斯算子。 特别是，我们将展示它们与经典麦克斯韦方程的紧密联系。 最后，我们将引入一种新的观点来定义玻色拉普拉斯算子，这简化了之前获得的玻色拉普拉斯算子与Rarita-Schwinger型算子之间的联系。 此外，得到一个矩阵型的Rarita-Schwinger算子，并提供了一些与此新型一阶矩阵型算子相关的结果。 显示英文摘要

摘要： In this article, we firstly introduce higher spin Clifford analysis, which are considered as generalizations of classical Clifford analysis by considering functions taking values in irreducible representations of the spin group. Then, we introduce a type of second order conformally invariant differential operators, named as bosonic Laplacians, in the higher spin Clifford analysis. In particular, we will show their close connections to classical Maxwell equations. At the end, we will introduce a new perspective to define bosonic Laplacians, which simplifies the connection between bosonic Laplacians and Rarita-Schwinger type operators obtained before. Moreover, a matrix type Rarita-Schwinger operator is obtained and some results related to this new first order matrix type operator are provided.