Related papers: Wigner Functions for Noncommutative Quantum Mechan…
Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of…
Infinitesimal holomorphic realizations for the Schr\"{o}dinger-Weil representation and the discrete series representations of the Jacobi group are constructed. Explicit expressions of the basic differential operators are obtained. The…
Extended Schwinger's quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold $M$ is a homogeneous Riemannian space with the given action of isometry transformation…
A symmetry in quantum mechanics is described by the projective representations of a Lie symmetry group that transforms between physical quantum states such that the square of the modulus of the states is invariant. The Heisenberg…
We study the representations of the quantum Galilei group by a suitable generalization of the Kirillov method on spaces of non commutative functions. On these spaces we determine a quasi-invariant measure with respect to the action of the…
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…
In this article we introduce a quasiprobability distribution of work that is based on the Wigner function. This construction rests on the idea that the work done on an isolated system can be coherently measured by coupling the system to a…
We propose a model of dynamical noncommutative quantum mechanics in which the noncommutative strengths, describing the properties of the commutation relations of the coordinate and momenta, respectively, are arbitrary energy dependent…
Quasiprobability representations, such as the Wigner function, play an important role in various research areas. The inevitable appearance of negativity in such representations is often regarded as a signature of nonclassicality, which has…
We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
Wigner's classification has led to the insight that projective unitary representations play a prominent role in quantum mechanics. The physics literature often states that the theory of projective unitary representations can be reduced to…
Mutually unbiased bases and discrete Wigner functions are closely, but not uniquely related. Such a connection becomes more interesting when the Hilbert space has a dimension that is a power of a prime $N=d^n$, which describes a composite…
Gaussian states have played on important role in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description.…
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 aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and…
One of the most prominent quasiprobability functions in quantum mechanics is the Wigner function that gives the right marginal probability functions if integrated over position or momentum. Here we depart from the definition of the…
We describe several different representations of nilpotent step two Lie groups in spaces of monogenic Clifford valued functions. We are inspired by the classic representation of the Heisenberg group in the Segal-Bargmann space of…
Starting with the first-order singular Lagrangian containing the redundant variables, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of the projection operator…