This paper focuses on the Popov generalized theory for a class of some linear systems including discrete and distributed delays. Sufficient conditions for stabilizing such systems as well as for coerciveness of an appropriate quadratic cost are developed. The obtained results are applied for the design of a memoiyless state feedback control law which guarantees the (exponential) closed-loop sta...

A criterion for the stability of control systems which contain an arbitrary jinik number oj memoryless nonlinearities is considered. The criterion is such that the degree oj stability may be specijied, and such that for the case when the absolute stability of a control system having one memoryless nonlinearity is considered, it reduces to the original Popov criterion. Introduction The formulati...

We consider how Lorentz-violating interactions in the Faddeev-Popov ghost sector will affect scalar QED. The behavior depends sensitively on whether the gauge symmetry is spontaneously broken. If the symmetry is not broken, Lorentz violations in the ghost sector are unphysical, but if there is spontaneous breaking, radiative corrections will induce Lorentz-violating and gauge-dependent terms in...

It is well known that in de Sitter space the (free) minimally coupled massless scalar field theory does not admit any de Sitter-invariant Hadamard state. Related to this is the fact that the prop-agator for the massive scalar field corresponding to the de Sitter-invariant vacuum state diverges in the massless limit, with the infrared-divergent term being a constant. Since the Faddeev-Popov ghos...

We derive the equations of time-independent stochastic quantization, without reference to an unphysical 5th time, from the principle of gauge equivalence. It asserts that probability distributions P that give the same expectation values for gauge-invariant ob-servables W = dA W P are physically indistiguishable. This method escapes the Gribov critique. We derive an exact system of equations tha...