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7 papers · 2 filters
Covariant geometric quantization of non-relativistic Hamiltonian mechanics
G. Giachetta, L. Mangiarotti, G. Sardanashvily
We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. This is a momentum phase space of non-relativistic mechanics…
Interacting Stochastic Process and Renormalization Theory
Yaroslav Volovich
A stochastic process with self-interaction as a model of quantum field theory is studied. We consider an Ornstein-Uhlenbeck stochastic process x(t) with interaction of the form x^{…
Quantum theory of self-action of ultrashort light pulses in an inertial nonlinear medium
F. Popescu, A. S. Chirkin
The systematic theory of the formation of the short light pulses in the squeezed state during the propagation in a medium with inertial Kerr nonlinearity is developed. The algebra…
Quantum mechanics with time-dependent parameters
G. Sardanashvily
Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in…
Self- and cross-phase modulation of ultrashort light pulses in an inertial Kerr medium: spectral control of squeezed light
F. Popescu, A. S. Chirkin
Quantum theory of self-phase and cross-phase modulation of ultrashort light pulses in the Kerr medium is developed with taking into account the response time of an electronic nonli…
Planar Dirac Electron in Coulomb and Magnetic Fields
Choon-Lin Ho, V. R. Khalilov
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values ar…