Related papers: Phase Space Quantum Mechanics
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum…
We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
In this paper we develop a method of constructing Hilbert spaces and the representation of the formal algebra of quantum observables in deformation quantization which is an analog of the well-known GNS construction for complex…
Using the notions of frame transform and of square integrable projective representation of a locally compact group $G$, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
Deformation quantization produces families of mathematically equivalent quantization procedures from which one must select the physically meaningful ones. As a selection principle we propose that the procedure must allow enough `observable'…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
In this paper, we demonstrate the equivalence between the complex Hilbert space and real Kahler space formulations of quantum mechanics. Complex numbers play an important role in the traditional formulation of quantum mechanics in complex…
W consider the problem of testing if a given matrix in the Hilbert space formulation of quantum mechanics or a function in the phase space formulation of quantum theory represent a quantum state. We propose several practical criteria to…
In our previous papers we were interested in making a reconstruction of quantum mechanics according to classical mechanics. In this paper we suspend this program for a while and turn our attention to a theme in the frontier of quantum…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is…
Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this paper explores the…
The paper provides an introduction into p-mechanics, which is a consistent physical theory suitable for a simultaneous description of classical and quantum mechanics. p-Mechanics naturally provides a common ground for several different…
In order to realize supersymmetric quantum mechanics methods on a four dimensional classical phase-space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal star-product in composing the components of…