论文标题
真正的希尔伯特空间中的Quaternionic标量场
Quaternionic scalar field in the real Hilbert space
论文作者
论文摘要
使用复杂的klein-gordon场作为模型，我们量化了真实希尔伯特空间中的Quaternionic标量场。因此，已经获得了拉格朗日的配方，以及哈密顿的配方以及能量和电荷运营商。相反，与复杂的情况相反，Quaternionic量化接受了两个量化方案，涉及两个或四个组件。因此，与复杂的标量场情况相比，Quaternionic场允许状态结构更丰富。此外，Quaternionic理论在其复杂成分中承认了进一步的新颖特征是一种非缔合代数结构，在复杂情况下未观察到这一点。
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and charge operators. Conversely to the complex case, the quaternionic quantization admits two quantization schemes, concerning either two or four components. Therefore, the quaternionic field permits a richer structure of states, if compared to the complex scalar field case. Moreover, the quaternionic theory admits as a further novel feature a non-associative algebraic structure in their complex components, something not observed in the complex case.
