  For a spacelike 2-surface in spacetime, we propose a new definition of
quasi-local angular momentum and quasi-local center of mass, as an element in
the dual space of the Lie algebra of the Lorentz group. Together with previous
defined quasi-local energy-momentum, this completes the definition of conserved
quantities in general relativity at the quasi-local level. We justify this
definition by showing the consistency with the theory of special relativity and
expectations on an axially symmetric spacetime. The limits at spatial infinity
provide new definitions for total conserved quantities of an isolated system,
which do not depend on any asymptotically flat coordinate system or asymptotic
Killing field. The new proposal is free of ambiguities found in existing
definitions and presents the first definition that precisely describes the
dynamics of the Einstein equation.
