Related papers: Why must we work in the phase space?

Conventional approach to quantum mechanics in phase space, (q,p), is to take the operator based quantum mechanics of Schrodinger, or and equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher…

We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…

We point out the conceptual problems related to the application of the standard notion of mass to quarks and recall the arguments that there should be a close connection between the properties of elementary particles and the arena used for…

In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In…

Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phase-space techniques are known, however a thorough…

Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches…

Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…

Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…

We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical…

After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions…

We look at the fundamental use of complex numbers in Quantum Mechanics (QM). A review of some of the most popular reasons given in the literature to support the necessity of the complex formalism, We add some insight by invoking others.…

The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…

We introduce a pedagogical discussion on Bohmian mechanics and its physical implications in connection with the important role played by the quantum phase in the dynamics of quantum processes. In particular, we focus on phenomena such as…

In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…

Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…

It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…

Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…

Phase plays a crucial role in many quantum effects including interference. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby…

The internal phase dynamics of a quantum system is revealed in details. Theoretical and experimental evidences of existence of a causal relation of the phase of the wave function with the dynamics of the quantum system are presented…

Classical and quantum world views differ in peculiar ways. Understanding decisive quantum features -- for which no classical explanation exist -- and their interrelations is of foundational interest. Moreover, recognizing non-classical…