论文标题
fermions与$ n $ dimensions的Palatini动作结合
Fermions coupled to the Palatini action in $n$ dimensions
论文作者
论文摘要
我们从拉格朗日和汉密尔顿的观点中研究了费米子与$ n $ dimensions（$ n \ geq 3 $）的最小和非最小值耦合。一般而言，所考虑的拉格朗日行动并不等于爱因斯坦 - 迪拉克动作原则。但是，通过正确选择耦合参数，可以在尺寸四的时空中给出与爱因斯坦 - 迪拉克理论完全等同的一阶动作。通过使用Vielbein的合适参数化和连接，给出了对一般拉格朗日的哈密顿分析，其中涉及明显的洛伦兹 - 偏置空间空间变量，实际的非规范符号结构，并且仅一流的约束。额外的汉密尔顿制剂是通过符号呈现的，其中一种涉及半敏化费米子。为了面对以前的方法，我们的结果是施加的。
We study minimal and nonminimal couplings of fermions to the Palatini action in $n$ dimensions ($n\geq 3$) from the Lagrangian and Hamiltonian viewpoints. The Lagrangian action considered is not, in general, equivalent to the Einstein-Dirac action principle. However, by choosing properly the coupling parameters, it is possible to give a first-order action fully equivalent to the Einstein-Dirac theory in a spacetime of dimension four. By using a suitable parametrization of the vielbein and the connection, the Hamiltonian analysis of the general Lagrangian is given, which involves manifestly Lorentz-covariant phase-space variables, a real noncanonical symplectic structure, and only first-class constraints. Additional Hamiltonian formulations are obtained via symplectomorphisms, one of them involving half-densitized fermions. To confront our results with previous approaches, the time gauge is imposed.
