On non-Abelian group of generalized covariant Hamilton system

This paper considers the non-abelian Lie algebra of Lie groups, by using the structure constant to construct some new quantities, the GCHS defined by GSPB \footnote{GPB:Generalized Poisson bracket; GHS:Generalized Hamilton System, GCHS:Generalized Covariant Hamilton System\\GSPB:Generalized structural Poisson bracket\\TGHS: thorough generalized Hamiltonian System} is for the covariant evolution equation that consists of two parts, TGHS and S dynamics. Meanwhile, the generalized force field given by the GCHS in terms of the momentum applies to deduce some results.Comment: 8 page

Geometric quantization rules in QCPB theory

Using the QCPB theory, we can accomplish the compatible combination of the quantum mechanics and general relativity supported by the G-dynamics. We further study the generalized quantum harmonic oscillator, such as geometric creation and annihilation operators, especially, the geometric quantization rules based on the QCPB theory.Comment: 14 page