Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum Mechanics

Fractional quantum mechanics

A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Levy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and s...

Quantum Mechanics in Infinite Symplectic Volume

We quantise complex, infinite–dimensional projective space CP(H). We apply the result to quantise a complex, finite–dimensional, classical phase space C whose symplectic volume is infinite, by holomorphically embedding it into CP(H). The embedding is univocally determined by requiring it to be an isometry between the Bergman metric on C and the Fubini–Study metric on CP(H). Then the Hilbert–spa...

Quark - Antiquark Bound

Asymmetric Quark/Antiquark Hadronization

We point out that the fragmentation of a strange quark into nucleons versus antinucleons is not necessarily identical Dp/s(z,Q ) 6= Dp/s(z,Q ), even though the perturbative contributions from gluon splitting and evolution are p ↔ p symmetric. The observation of such asymmetries in the hadronization of strange and other heavy quarks can provide insight into the nonperturbative mechanisms underly...

- quark - antiquark potential

We calculate the leading mass-suppressed two-loop contribution, proportional to αs/(mqr 2), to the potential of a heavy quark-antiquark system. This contribution originates in the nonabelian nature of quantum chromodynamics (QCD) and has no analogue in quantum electrodynamics (QED). For this purpose, we elaborate a technique based on the implementation of the threshold expansion within the effe...