On the hermiticity of q-differential operators and forms on the quantum Euclidean spaces R_q^N

Details On the hermiticity of q-differential operators and forms on the quantum Euclidean spaces R_q^N On the hermiticity of q-differential operators and forms on the quantum Euclidean spaces R_q^N

2004-03-26

arxiv.org/abs/math/0403463v3

Rev.Math.Phys.18:79-117,2006

Mathematics

Quantum Algebra

Latex file, 40 pages, 1 built in figure. Added references. Final version to appear in Rev. Math. Phys

Scientific paper

10.1142/S0129055X06002590

We show that the complicated *-structure characterizing for positive q the U_qso(N)-covariant differential calculus on the non-commutative manifold R_q^N boils down to similarity transformations involving the ribbon element of a central extension of U_qso(N) and its formal square root v. Subspaces of the spaces of functions and of p-forms on R_q^N are made into Hilbert spaces by introducing non-conventional ``weights'' in the integrals defining the corresponding scalar products, namely suitable positive-definite q-pseudodifferential operators realizing the action of v^{\pm 1}; this serves to make the partial q-derivatives antihermitean and the exterior coderivative equal to the hermitean conjugate of the exterior derivative, as usual. There is a residual freedom in the choice of the weight m(r) along the `radial coordinate' r. Unless we choose a constant m, then the square-integrables functions/forms must fulfill an additional condition, namely their analytic continuations to the complex r plane can have poles only on the sites of some special lattice. Among the functions naturally selected by this condition there are q-special functions with `quantized' free parameters.

Affiliated with

Also associated with

No associations

Rating

On the hermiticity of q-differential operators and forms on the quantum Euclidean spaces R_q^N 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 On the hermiticity of q-differential operators and forms on the quantum Euclidean spaces R_q^N, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the hermiticity of q-differential operators and forms on the quantum Euclidean spaces R_q^N will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-383594