论文标题
庞加莱集团无质量统一表示的捆绑结构
Bundle Structure of Massless Unitary Representations of the Poincaré Group
论文作者
论文摘要
回顾了四维时空的庞加莱组的诱发表示形式的构建，我们发现了所有巨大的表示，包括在相互作用的多个粒子状态下进行的。非散热螺旋性的无质量动量波形被证明是u（1） - 捆绑物上的块壳上的块，这是迄今为止在括号符号中被忽略的属性。我们的传统符号启用了有关正方形的集成性和光滑度的问题。他们的答案完成了相对论量子物理学的图片。 Frobenius的互惠定理禁止无质量的单粒子状态，其总角动量小于螺旋度的模量。没有两光子状态具有j = 1，可以解释正交定位的寿命。 动量波函数的部分衍生物不是可将其用于无逆螺旋性的无质量状态PSI的算子。它们仅允许协变量，非公认衍生物。无质量的壳具有非交通性的几何形状，其螺旋性是其拓扑电荷。 PSI的空间位置操作员构成了Heisenberg与空间动量对，被Lorentz Generator的域的平滑性要求排除在外。
Reviewing the construction of induced representations of the Poincaré group of four-dimensional spacetime we find all massive representations, including the ones acting on interacting many-particle states. Massless momentum wavefunctions of non-vanishing helicity turn out to be more precisely sections of a U(1)-bundle over the massless shell, a property which to date was overlooked in bracket notation. Our traditional notation enables questions about square integrability and smoothness. Their answers complete the picture of relativistic quantum physics. Frobenius' reciprocity theorem prohibits massless one-particle states with total angular momentum less than the modulus of the helicity. There is no two-photon state with J=1, explaining the longevity of orthopositronium. Partial derivatives of the momentum wave functions are no operators which can be applied to massless states Psi with nonvanishing helicity. They allow only for covariant, noncommuting derivatives. The massless shell has a noncommutative geometry with helicity being its topological charge. A spatial position operator for Psi which constitutes Heisenberg pairs with the spatial momentum, is excluded by the smoothness requirement of the domain of the Lorentz generators.
