Fuzzy space-time topology and geometric quantization

Fuzzy Phase Space and Space-time Structure as Approach to Quantization

The quantum space-time and the phase space of massive particles with Fuzzy Geometry structure investigated as the possible quantization formalism. In this model the state of nonrelativistic particle m corresponds to the element of fuzzy ordered set (Foset)-fuzzy point. Due to its partial ordering m space coordinate x acquires principal uncertainty σ x. It's shown that Fuzzy Mechanics (FM) in 1+...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Space-Time Quantization and Matrix Model

In order to get the general framework describing a nonlocalizable object beyond the bilocal field theory early proposed by Markov and Yukawa, the quantization of space-time is reconsidered and further developed. Space-time quantities are there not only noncommutative with U -field describing the nonlocalizable object, as in the bilocal field theory, but also become noncommutative among themselv...

Casimir effect on nontrivial topology spaces in Krein space quantization

Casimir effect of a topologically nontrivial two-dimensional space-time, through Krein space quantization [1, 2], has been calculated. In other words, auxiliary negative norm states have been utilized here. Presence of negative norm states play the role of an automatic renormalization device for the theory. The negative norm states (which do not interact with the physical world) could be chosen...

Topology and Quantization ∗

A simple algebraic model of charged particle coupled to singular magnetic field is given. Quantization is described as gradation by certain abelian group G. Statistics is determined by a commutation factor λ on the grading group G. Composite fermions and composite bosons are described in an unified way as Z 2 ⊕ ... ⊕ Z 2-graded λ-commutative algebras.