Gauge Theory in the Quantum Phase Space CP ( N - 1 )

The ordinary linear quantum theory predicts the quantum correlations at any distance (the universal superposition principle). It creates the decoherence problem since quantum interactions entangle states into non-separable combination. On the other hand the linear quantum theory prevents the existence of the localizable solutions , and after all, leads to the divergences problem in the quantum field theory. In order to overcome these difficulties the non-perturbative nonlinearity originated by the curvature of the compact quantum phase space (QPS) has been used. PACS numbers: 03.65.Ca, 03.65.Ta Non-linearity in quantum theory has been invoked in order to build the objective quantum theory and to prevent the unlimited spread out of the observable fields by the gravitational self-potential [1, 2]. But Newtonian quantum gravity in the present form is not effective for the shaping wave-packets of elementary particle size since the characteristic scale of the ground-state wave-packet obtained from the gravitational Schrödinger equation for nucleon masses is around 10 23 m [2]. There is a different group of works make accent on the formulation of the standard quantum mechanics in QPS represented by the complex projective Hilbert space CP (N − 1) [3, 4, 5, 6, 7]. I think, however, that consistent and prolific theory based on such QPS should be connected with serious deviations from the standard quantum scheme. Such modification must, of course, preserve all achievements of de Broglie-Heisenberg-Schrödinger-Dirac linear theory by a natural way. One may think about attempts to establish a deductive approach to the quantum theory. 1 General part.— The classical field theory treats the 'fields' as force functions of the space-times coordinates with pointwise action on the probe particles. It is assumed this picture has clear macroscopic sense. Nevertheless, the classical field theory is contradictable since it is impossible to describe the stable charged particles in its own framework. Quantum particle like electron is pointwise but it is 'wrapped' in so-called de Broglie-Schrödinger fields of probability. Quantum field theory (QFT) uses same classical space-time coordinates as 'index' whereas the fields are operators acting in some Hilbert state space (frequently in Fock space). Quantum mechanics and QFT make accent on the non-commutative nature of the dynamical variables but the interaction between pointwise particles and the relativistic invariance are borrowed from the classical theory. These are the sources of the singular functions involved in QFT. All attempts to build realistic extended stable model of an elementary particles in the …