Bohr-Sommerfeld Quantization of Spin Hamiltonians

Bohr-Sommerfeld conditions for several commuting Hamiltonians

Bohr-Sommerfeld quantization of periodic orbits.

We show, that the canonical invariant part of h̄ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable systems. We argue that the information content of the classical action and stability can be used more effectively than in the usual treatment. We demonstrate the imp...

Bohr-Sommerfeld quantization and meson spectroscopy

We use the Bohr-Sommerfeld quantization approach in the context of constituent quark models. This method provides, for the Cornell potential, analytical formulas for the energy spectra which closely approximate numerical exact calculations performed with the Schrödinger or the spinless Salpeter equations. The Bohr-Sommerfeld quantization procedure can also be used to calculate other observables...

Discreteness of the volume of space from Bohr-Sommerfeld quantization.

A major challenge for any theory of quantum gravity is to quantize general relativity while retaining some part of its geometrical character. We present new evidence for the idea that this can be achieved by directly quantizing space itself. We compute the Bohr-Sommerfeld volume spectrum of a tetrahedron and show that it reproduces the quantization of a grain of space found in loop gravity.

Bohr-sommerfeld Star Products

We relate the Bohr-Sommerfeld conditions established in λ-microlocal analysis to formal deformation quantization of symplectic manifolds by classifying star products adapted to some Lagrangian sub-manifold L, i.e. products preserving the classical vanishing ideal IL of L up to IL-preserving equivalences.