TENTANG PENGKUANTUMAN GEOMETRIK DAN TERAPANNYA UNTUK BEBERAPA SISTEM FISIS; ON GEOMETRIC QUANTIZATION AND ITS APPLICATION TO SOME PHYSICAL SYSTEM

Tampi, Emma M, Muhammad Farchani Rosyid

2015 | Skripsi | FMIPA

The theory of geometric quantization has been explained. A few aspects related to geometric quantization consist of mathematical tools required for geometric quantization, such as symplectic vector space, symplectic manifold, forms, real distribution and the complex one, and complex structure have been considered. Then the procedure of geometric quantization and its application have been considered. In this first step, Hilbert space containing cross sections - bundle of complex line with Hermitean connection - has been constructed. Then, in the second step polarization has been done. In this step, limitation of Hilbert space by choosing the type of cross section which is used has been done. The later is the step of metaplectic correction, in certain cases, the step of polarization is not sufficient because volume form which is used on pre-quantization can not be used anymore after polarization. In this step, pre-quantum bundle which has been polarized then arranged in a such way that volume form problem can be solved. This method of quntization is then applied to few real cases.

Kata Kunci : manifold; line bundle; form; connection; parallel transport; and section