Deformation Quantization: Quantum Mechanics Lives & Works in Phase-Space скачать в хорошем качестве

Deformation Quantization: Quantum Mechanics Lives & Works in Phase-Space

Cosmas Zachos , Colloquium at the Physics Dept of the University of Miami, Oct 14, 2020. Wigner's 1932 quasi-probability Distribution Function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum flows in: semiclassical limits; quantum optics; nuclear physics; decoherence (eg, quantum computing); quantum chaos; "Welcher Weg" puzzles. It is also of importance in signal processing (time-frequency analysis). Nevertheless, a remarkable aspect of its internal logic, pioneered by J Moyal, and H Groenewold, has only emerged in this millennium: It furnishes a third, alternate, formulation of Quantum Mechanics, independent of the conventional Hilbert Space, or Path Integral formulations, and perhaps more intuitive, since it shares language with classical mechanics. It is logically complete and self-standing, and accommodates the uncertainty principle in an unexpected manner. 00:00 Introduction & Wigner Function 17:00 Negative values & the Uncertainty Principle 20:40 Well ordering; Expectation Values; Star Product; Moyal Brackets 28:15 Star-genvalue Equations 41:50 SHOscillator 51:10 Time Evolution