The foundations of quantum theory and its possible generalizations

Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the statistical operator is reviewed. The Tomonaga-Schwinger like equation of this type is introduced to establish Lorentz invariance. The application of tachyonic field to overcome divergences arising in this equation is analyzed. Other approaches to the problem are shortly discussed.