Related papers: Sp(2,$\mathbb{Z}$) invariant Wigner function on ev…
Suppose $\phi_3:Sp(1)\rightarrow Sp(2)$ denotes the unique irreducible $4$-dimensional representation of $Sp(1) = SU(2)$ and consider the two subgroups $H_1, H_2\subseteq Sp(3)$ with $H_1 = \{\operatorname{diag}(\phi_3(q_1), q_1): q_1 \in…
Given an oriented surface S with base point * on the boundary, we introduce for all N>0, a canonical quasi-Poisson bracket on the space of N-dimensional linear representations of \pi_1(S,*). Our bracket extends the well-known Poisson…
We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space', and `Wigner distributions'; for finite dimensional quantum systems. For such systems, where traditional concepts of `momenta' established for…
It is common knowledge that the Wigner function of a quantum state may admit negative values, so that it cannot be viewed as a genuine probability density. Here, we examine the difficulty in finding an entropy-like functional in phase space…
An integral of the Wigner function of a wavefunction |psi >, over some region S in classical phase space is identified as a (quasi) probability measure (QPM) of S, and it can be expressed by the |psi > average of an operator referred to as…
Let $M$ be a Hopf--von Neuman algebra with the predual $M_*$ and $WAP(M)$ the subspace in $M$ composed of weakly almost periodic functionals on $M_*$. The main example of such an algebra is $M=L^\infty(\mathbb G)$ for a locally compact…
We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations, which includes the known bosonic and discrete Wigner functions. We characterize the groups of quantum unitary…
Hwang's quasi-power theorem asserts that a sequence of random variables whose moment generating functions are approximately given by powers of some analytic function is asymptotically normally distributed. This theorem is generalised to…
We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them.
The concern of this article is a semiclassical Weyl calculus on an infinite dimensional Hilbert space $H$. If $(i, H, B)$ is a Wiener triplet associated to $H$, the quantum state space will be the space of $L^2$ functions on $B$ with…
We investigate refined algebraic quantisation with group averaging in a finite-dimensional constrained Hamiltonian system that provides a simplified model of general relativity. The classical theory has gauge group SL(2,R) and a…
We define and study distributions in R^{d} that we call q-Normal. For q=1 they are really multidimensional Normal, for q\in(-1,1) they have densities, compact support and many properties that resemble properties of ordinary multidimensional…
An embedding method to get $q$-deformations for the non--semisimple algebras generating the motion groups of $N$--dimensional flat spaces is presented. This method gives a global and simultaneous scheme of $q$-deformation for all $iso(p,q)$…
In this study, we compare the Wigner function $W$, its modulus, and the Husimi distribution $H$ in a one-dimensional quantum system exhibiting a transition from a single-well to a double-well configuration, using the quasi-exactly solvable…
The Wigner distribution function is a quasi-probability distribution. When properly integrated, it provides the correct charge and current densities, but it gives negative probabilities in some points and regions of the phase space.…
Wigner's celebrated theorem, which is particularly important in the mathematical foundations of quantum mechanics, states that every bijective transformation on the set of all rank-one projections of a complex Hilbert space which preserves…
We determine a positive normalised phase space probability distribution $P$ with minimum mean square fractional deviation from the Wigner distribution $W$ .The minimum deviation, an invariant under phase space rotations, is a quantitative…
Quasicrystals are tempered distributions $\mu$ which satisfy symmetric conditions on $\mu$ and $\widehat \mu$. This suggests that techniques from time-frequency analysis could possibly be useful tools in the study of such structures. In…
We study, in a global uniform manner, the quotient of the ring of polynomials in l sets of n variables, by the ideal generated by diagonal quasi-invariant polynomials for general permutation groups W=G(r,n). We show that, for each such…
We investigate the relationship between two properties of quantum transformations often studied in popular subtheories of quantum theory: covariance of the Wigner representation of the theory and the existence of a transformation…