Classical and quantum descriptions of a nonlocal confined particle—Quarks

Some aspects of classical and quantum theories of quarks, gluons, and their interaction mechanisms are considered within the framework of stochastic space-time, which is induced by a random string field. It turns out that quarks and gluons are extended objects, the propagators of which are entire functions in the momentum space. It is shown that the topological structure of space-time inside hadrons plays an essential role in quark confinement and asymptotic freedom. The strong coupling constant and confinement potential, mass, and energy of quarks depend on the Euler number, which gives rise to a unified description of the interaction picture in QCD at short and long distances. Quantization of nonlocal quark fields is achieved by using an indefinite metric, and their electromagnetic nonlocal interaction is also considered.