Geometric momentum and angular momentum for charge-monopole system

Angular momentum and wave functions in monopole and related potentials.

In a three-dimensional context, it is shown how wave functions may be chosen from among the solutions of the Schrodinger equation in a consistent way without demanding single valuedness, but by imposing an invariance condition on the domain of certain given linear operators. This leads to multiple-valued wave functions in certain situations, but disallows unquantized monopoles and "unusual" ang...

angular-momentum, and charge inequalities for axisymmetric initial data

We present the key elements of the proof of an upper bound for angular-momentum and charge in terms of the mass for electro-vacuum asymptotically flat axisymmetric initial data sets with simply connected orbit space.

Angular Momentum

Rotations and Angular Momentum

2 Exercise. Prove it. ◦ In fact, as sophisticates can show you, on a complex space a linear operator which preserves all norms will also preserve all inner products. But the key thing is to remember is that a unitary operator preserves all inner products (and therefore all norms). • This is analogous to the fact that translations and rotations in ordinary three-dimensional space preserve distan...

Rotation and Angular Momentum

There is a fundamental connection between the angular momentum (a mechanical quantity) and the rotation operators (which is a symmetry group). The angular momentum is the generator of rotations. Because of this connection, many properties of angular momentum operators can be derived from the properties of the rotation group. We will derive these properties (mainly the commutation relations) sta...