O použití Einsteinových rovnic v kosmologii
Formulating the two-body problem of classical relativistic electrodynamics in terms of action at a distance and using retarded potential, the equations of one-dimensional motion are functional differential equations of the retarded type. For this kind of equations, in general it is not enough to specify instantaneous data to specify unique trajectories. Nevertheless, Driver (1969) has shown that under special conditions for these electrodynamic equations, there exists an unique solution for this...
We discuss a recent approach to quantum field theoretical path integration on noncommutative geometries which imply UV/IR regularising finite minimal uncertainties in positions and/or momenta. One class of such noncommutative geometries arise as `momentum spaces' over curved spaces, for which we can now give the full set of commutation relations in coordinate free form, based on the Synge world function.
One studies the differential equations of the movement of certain classical and relativistic systems for some special Lagrangian functions. One considers particularly the case in which the problem presents cyclic coordinates. Some electrodynamical applications are studied.