Electrodynamics in quantum space-time (Q1093941)

It is shown that introducing quantum space-time into physics leads to a certain fictitious ``gravitational'' field with the ``metric tensor'' \(\hat g_{\mu \nu}(z)\). This formalism allows us to reformulate Maxwell's equations in quantum space-time in accordance with the general covariance principle. A transformation method connecting the electromagnetic field tensor \(\hat F^{\mu \nu}(z)\) to the usual one \(F^{\mu \nu}(x)\) for the quantum system of reference is given. The electromagnetic force acting on the charged particle in quantum space- time is also defined and its equation of motion is investigated for a concrete case. In our scheme, a gauge-invariant description of electromagnetic processes in quantum space-time at small distances is achieved by using gauge transformations over the whole space-time on the large scale.