Related papers: Perspectives: Quantum Mechanics on Phase Space
It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of…
In this paper we study the structure of the phase space in noncommutative geometry in the presence of a nontrivial frame. Our basic assumptions are that the underlying space is a symplectic and parallelizable manifold. Furthermore, we…
Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra.
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the…
The metric structure of homogeneous spaces of rank-one and rank-two associated to the real pseudo-orthogonal groups SO(p,q) and some of their contractions (e.g., ISO(p,q), Newton-Hooke type groups...) is studied. All these spaces are…
Fundamental representations of real simple Poisson Lie groups are Poisson actions with a suitable choice of the Poisson structure on the underlying (real) vector space. We study these (mostly quadratic) Poisson structures and corresponding…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
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…
We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic…
In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality.
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
We present a general theory of quasiprobability distributions on phase spaces of quantum systems whose dynamical symmetry groups are (finite-dimensional) Lie groups. The family of distributions on a phase space is postulated to satisfy the…
We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence…
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…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
Despite the impressive amount of literature on the foundations of quantum mechanics, the relevance of symmetry in interpretation is not properly acknowledged. In fact, although it is usually said that quantum mechanics is invariant under…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective…