论文标题
圆锥路径约束二等系统的一般解决方案和规范量化
General Solution and Canonical Quantization of the Conic Path Constrained Second-Class System
论文作者
论文摘要
我们考虑在给定外部电势函数下沿圆锥路径受约束运动的问题。该模型被描述为二等系统，捕获了特定量子场理论一类的行为。通过表现出合适的整合因子，我们获得了相关非线性微分方程的一般解决方案。我们以相应的狄拉克括号以一致的方式执行规范量化。我们将Dirac-Bergmann算法应用于其动态汉密尔顿描述固有的整个内部约束结构，获得适当的扩展汉密尔顿功能，确定Lagrange乘数并计算所有相关的Poisson Brackets，Hamiltonian和Lagrange多派。明确获得了相位空间中的完整狄拉克支架代数及其在差分运算符方面的物理实现。
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By exhibiting a suitable integration factor, we obtain the general solution for the associated non-linear differential equations. We perform the canonical quantization in a consistent way in terms of the corresponding Dirac brackets. We apply the Dirac-Bergmann algorithm to unravel and classify the whole internal constraints structure inherent to its dynamical Hamiltonian description, obtain the proper extended Hamiltonian function, determine the Lagrange multiplier and compute all relevant Poisson brackets among the constraints, Hamiltonian and Lagrange multiplier. The complete Dirac brackets algebra in phase space as well as its physical realization in terms of differential operators is explicitly obtained.
