Recommendation for "Formula of angular momentum" by Takehiko Tanaka

Brownian motion, reflection groups and Tanaka formula

In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the decomposition we obtain may be seen as a multidimensional extension of Tanaka’s formula for linear Brownian motion. The paper is closed with a description of the boun...

Angular Momentum

SWKB for the Angular Momentum

It has been recently shown [M. Robnik and L. Salasnich, J. Phys. A: Math. Gen., 30, 1719 (1997)] that the WKB series for the quantization of angular momentum L converges to the exact value L = h̄l(l + 1), if summed over all orders, and gives the Langer formula L = h̄(l + 1/2) at the leading order. In this work we solve the eigenvalue problem of the angular momentum operator by using the supersymm...

Spin Angular Momentum Imparted by Gravitational Waves

Following the demonstration that gravitational waves impart linear momentum, it is argued that if they are polarized they should impart angular momentum to appropriately placed 'test rods' in their path. A general formula for this angular momentum is obtained and used to provide expressions for the angular momentum imparted by plane and cylindrical gravitational waves. While the plane [1] and c...

Angular momentum generation by parity violation

We generalize our holographic derivation of spontaneous angular momentum generation in 2 + 1 dimensions in several directions. We consider cases when a parity-violating perturbation responsible for the angular momentum generation can be nonmarginal (while in our previous paper we restricted to a marginal perturbation), including all possible two-derivative interactions, with parity violations t...