Energy, Momentum and Angular Momentum in Poincare Gauge Theory

Abstract

In Poincaré gauge theory we explore the relations between differential conservation laws and integral conserved quantities. In particular, we investigate in details spin angular-momentum complex for an isolated system whose boundary at infinity is Minkowskian, by the generator method mutatis mutandis. It is shown that two separately conserved quantities (spin and orbital angular momenta) integrated over whole space diverge, and that their sum, called the total angular momentum, has a convergent expression which is conserved and well-defined. Similar discussion is also made on energy and momentum of the system. We exhibit the asymptotic behavior of the translation and Lorentz gauge fields, and calculate relevant superpotentials explicitly. We briefly sketch the case of asymptotically “non-flat” spacetime.