arXiv subjects
Publications and source records attributed to Nik. Tyurin.
This small note contains two simple remarks about Bohr - Sommerfeld with respect to the anticanonical class lagrangian tori in the projective spaces, which are the most popular examples of monotone symplectic manifolds.
In the present text we discuss basic aspects of the Seiberg - Witten theory mainly focusing the attantion on some geometrical details which could make the introduction to the subject more illustrative. At the same time we list there natural problems arise in this framework mostly interesting to the author. This text could be regarded as additional remarks to any comlete course on the Seiberg - Witten invariants.
This paper proposes a new way to quantize classical mechanical systems. Here we use ALAG - programme to construct moduli space of half weighted Bohr - Sommerfeld lagrangian cycles of fixed volume which is our quantum phase space. "Dynamical correspondence" principle makes possible to prove that this ALAG - quantization satisfies the Dirac correspondence principle. This construction relates two known quantizations using complex and real polarizations respectively.
It was pointed out that the space of hermitian triples is an anology of the hermitian connection space. Generalizing the Ashtekar - Isham procedure one can quantize the space of hermitian triples as well as the original one. Here we add an example how this similarity can be exploited in a quantum theory of riemannian geometry.