平移引力规范理论中的能量动量及其哈密顿表述

Gravitational Energy-momentum and the Hamiltonian Formulation of the Teleparallel Gravity

分析了平移引力规范理论中引力场的能量动量的变换特性 ,证明了引力场的能量动量可以表示为洛仑兹规范势的二次齐式因而在局域洛仑兹变换下不协变 .另一方面 ,引力场的能量动量又可以表示为平移规范场强的二次齐式因而在广义坐标变换下协变 .给出平移引力规范理论的一个新的简化的哈密顿表述 ,其约束代数与广义相对论的约束代数形式相同 ,从而证明了平移引力规范理论与广义相对论在哈密顿表述下的等价性 .

The transformation properties of the gravitational energy momentum in the teleparallel gravity are analyzed.It is proved that the gravitational energy momentum in the teleparale gravity can be expressed in terms of the Lorentz gauge potential and therefore is not covariant under local Lorentz transformations.On the other hand,it can also be expressed in terms of the translation gauge field strength and therefore is covariant under general coordinate transformations.A simplified Hamiltonian formulation of the teleparallel is given.Its constraint algebra has the same structure as that of general relativity,which indicates the equivalence between the teleparallel grivity and general relativity in the Hamiltonian formulation.