Talk detail

Participant	Mayburov, Sergey
Institution	Lebedev inst. of Physics - Leninsky pr., 53 - Moscow - Moscow region - Russia

Session	QG1	Accepted		Order	Time
Talk	Oral abstract	Title	Fuzzy Space-time, Quantization and Gauge Invariance
Co-authors
Abstract	Dodson-Zeeman fuzzy topology (FT) is studied as quantum space-time formalism. FT elements are fuzzy points (FP) {ai}, beside standard orderimg relation aj ¡Ü ak, they admit also the incomparability relation(IR)between them: aj ~ ak, so their set Ap is partial-ordered set (Poset). For 1-dimensional geometry Universe is supposedly Poset U=Ap+X, where X is coordinate axe R1, so that aj ~ x permitted for some x of X. ai properties are detalized by introduction of fuzzy weight w(x) ¡Ý 0 with norm 1. FP a(t) supposedly describes massive particle ¦Ì, its coordinate on X is principally uncertain. ¦Ì state denoted ¦Õ(x,t), its free parameter is w flow velocity v(x), in x-representation it transformed to ¦Á(x)corresponding to ¦Õ(x,t) phase. It's shown that ¦Õ(x,t) evolution obeys to free Schroedinger equation. In relativistic case free ¦Ì evolution is described by Dirac equation with spin-half. Commutation relations [x, p]=i are derived from topological premises; construction of Lorentz-covariant noncommutative geometry is considered. Interactions of massive particles on fuzzy manifold are studied, and shown to be gauge invariant. In particular, interactions of fermion muliplets are performed by corresponding Yang-Mills fields.