Related papers: Why must we work in the phase space?
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
Phase is a basic ingredient for quantum states since quantum mechanics uses complex numbers to describe quantum states. In this letter, we introduce a rigorous framework to quantify the phase of quantum states. To do so, we regard phase as…
The notion of phase plays an esential role in both classical and quantum mechanics.But what is a phase? We show that if we define the notion of phase in phase (!) space one can very easily and naturally recover the Heisenberg-Weyl…
A phase space mathematical formulation of quantum mechanical processes accompanied by and ontological interpretation is presented in an axiomatic form. The problem of quantum measurement, including that of quantum state filtering, is…
The phase-space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including metho ds of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase…
Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold…
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical…
Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…
Phase-space techniques are generalized to nonlinear quantum electrodynamics beyond the rotating wave approximation, resulting in an essentially classical picture of radiation dynamics.
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
Phase-space path-integrals are used in order to illustrate various aspects of a recently proposed interpretation of quantum mechanics as a gauge theory of metaplectic spinor fields.
Informal collection of lecture notes introducing quantum mechanics in phase space and basic Gaussian quantum mechanics.