Lagrangian form of Schr\"odinger equation

Lagrangian formulation of quantum mechanical Schr\"odinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system results in a well defined second order equation on a real vector space. The Klein-Gordon equation for a real field is shown to be the Lagrangian form of the corresponding Schr\"odinger equation.Comment: To appear in Foundation of Physic

The one-loop renormalization of the gauge sector in the noncommutative standard model

In this paper we construct a version of the standard model gauge sector on noncommutative space-time which is one-loop renormalizable to first order in the expansion in the noncommutativity parameter $\theta$. The one-loop renormalizability is obtained by the Seiberg-Witten redefinition of the noncommutative gauge potential for the model containing the usual six representations of matter fields of the first generation.Comment: 16 pages, 2 figure

Time delay in a basic model of the immune response

The efcts of time delay on the two-dimensional system of Mayer et al., which represents the basic model of the immune response,are analysed (cf. Mayer H, Zaenker KS, an der Heiden U. A basic mathematical model of the immune response. Chaos, Solitons and Fractals 1995;5:155 We studied variations of the stability of the occurrence of the chaotic solutions

Geometric Phase of an Open System

Quantum state diffusion unraveling of the Linblad master equation is utilized to define a geometric phase of an open quantum system. It is then shown that such geometric phase is invariant under unitary symmetry transformations of the Linblad equation, which is important property not shared by the geometric phases based on other types of unraveling