A Study of Generalized Covariant Hamilton Systems On Generalized Poisson manifold

Since the basic theoretical framework of generalized Hamilton system is not perfect and complete, there are often some practical problems that can not be expressed by generalized Hamilton system. The generalized gradient operator is defined by the structure function on manifold to improve the basic theoretical framework of the whole generalized Hamilton system. The generalized structure Poisson bracket is defined as well on manifolds. The geometric bracket is also given, and the covariant extension form of the generalized Hamilton system directly related to the structure function, the generalized covariance, is further obtained--generalized covariant Hamilton system, It includes thorough generalized Hamiltonian system and S-dynamic system.Comment: 15 page

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