报告题目：Gravitational energy for GR and Poincare gauge theories: A covariant Hamiltonian approach
报告人：James M. Nester (中央大学教授)
We want to consider, for gravitating systems, how to best describe energy–momentum and angular momentum/center-of-mass momentum. These quantities cannot be given by a local density. The modern understanding is that (i) they are quasi-local (associated with a closed 2-surface), (ii) they have no unique formula, (iii) they have no reference frame independent description. Firstly, we review some early history on the subject of gravitational energy in Einstein’s general relativity (GR), noting especially Noether’s contribution. Secondly, we review much of our covariant Hamiltonian formalism and apply it to Poincar′e gauge theories of gravity(PG), with GR as a special case. The Hamiltonian boundary term has two roles, it determines the quasi-local quantities, and furthermore, it determines the boundary conditions for the dynamical variables. Energy–momentum and angular momentum/CoMM are associated with the geometric symmetries under Poincar′e transformations. They are best described in a local Poincar′e gauge theory. The type of spacetime that naturally has this symmetry is Riemann–Cartan spacetime, with a metric compatible connection having, in general, both curvature and torsion. Thus our expression for the energy–momentum of physical systems is obtained via our covariant Hamiltonian formulation applied to the PG.
James M. Nester，中央大学物理系教授，理学博士（Maryland University），从事广义相对论的研究。