Physics – Quantum Physics
Scientific paper
2005-05-19
J.Phys.A: Math.Gen., 2005, v.38, 8549-8578
Physics
Quantum Physics
Latex, 38 pages, 5 figures, minor corrections
Scientific paper
10.1088/0305-4470/38/40/006
For manifolds $\cal M$ of noncompact type endowed with an affine connection (for example, the Levi-Civita connection) and a closed 2-form (magnetic field) we define a Hilbert algebra structure in the space $L^2(T^*\cal M)$ and construct an irreducible representation of this algebra in $L^2(\cal M)$. This algebra is automatically extended to polynomial in momenta functions and distributions. Under some natural conditions this algebra is unique. The non-commutative product over $T^*\cal M$ is given by an explicit integral formula. This product is exact (not formal) and is expressed in invariant geometrical terms. Our analysis reveals this product has a front, which is described in terms of geodesic triangles in $\cal M$. The quantization of $\delta$-functions induces a family of symplectic reflections in $T^*\cal M$ and generates a magneto-geodesic connection $\Gamma$ on $T^*\cal M$. This symplectic connection entangles, on the phase space level, the original affine structure on $\cal M$ and the magnetic field. In the classical approximation, the $\hbar^2$-part of the quantum product contains the Ricci curvature of $\Gamma$ and a magneto-geodesic coupling tensor.
Karasev Mikhail V.
Osborn T. A.
No associations
LandOfFree
Cotangent bundle quantization: Entangling of metric and magnetic field does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Cotangent bundle quantization: Entangling of metric and magnetic field, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cotangent bundle quantization: Entangling of metric and magnetic field will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-582309