Feynman Integral and Random Dynamics in Quantum Physics: A Probabilistic Approach to Quantum Dynamic

Foreword. Introduction. Basic Notation. 1. Preliminaries. 2. Markov chains. 3. Stochastic differential equations. 4. Semi-groups and the Trotter product formula. 5. The Feynman integral. 6. Feynman integral and stochastic differential equations. 7. Random perturbations of the classical mechanics. 8. Complex dynamics and coherent states. 9. Quantum non-linear oscillations. 10. Feynman integral on analytic submanifolds. 11. Interaction with the environment. 12. Lindblad equation and stochastic Schrödinger equation. 13. Hamiltonian time evolution of the density matrix. 14. Stochastic representation of the Lindblad time evolution. 15. Decoherence and estimates on dissipative dynamics. 16. Diffusive behaviour of the Wigner function and decoherence. 17. Scattering and tunnelling in an environment. 18. The Feynman integral in quantum field theory. 19. The phase space methods in QFT. 20. Computer simulations of quantum random dynamics. Bibliography. Index.