TENTANG GEOMETRISASI DAN PENGKUANTUMAN GEOMETRIK PADA TEORI MEDAN RELATIVISTIK; ON THE GEOMETRIZATION AND GEOMETRIC QUANTIZATION OF RELATIVISTIC FIELD THEORY

Listiyanto, M. Farchani Rosyid

2015 | Disertasi | FMIPA

The geometrization of relativistic field theories and their geometric quantization has been carried out on basis of the study of infinite dimensional symplectic manifold and dynamical system, especially on those aspects that distinguishes it from the finite one. The different aspects are weak non-degenerate and strong non-degenerate concepts, the failure of the Darboux theorem and problems on differentability of flows. The geometrization is obtained by assuming that the space of solution is an infinite dimensional symplectic manifold in which the symplectic structure is constructed from the Lagrangian density of the system. The geometrization of interacting system is also studied, especially the interaction between gauge field and relativistic field. Furthermore, the geometric quantization method is applied on symplectic manifold which is yielded from the geometrization procedure, so that the quantum field description is obtained.

Kata Kunci : geometrization; symplectic manifold; solution space; geometric quantization