Related papers: Wigner Functions on a Lattice
We examine the applicability and viability of methods to obtain knowledge about bound-states from information provided solely in Euclidean space. Rudimentary methods can be adequate if one only requires information about the ground and…
In this note, we extend the results about the fluctuations of the matrix entries of regular functions of Wigner random matrices obtained in arXiv:1103.3731 [math.PR] to Wigner matrices with non-i.i.d. entries provided certain Lindeberg type…
Similarly to the interaction lagrangian, the possible boundary conditions in quantum field theories on space-time manifolds with boundaries are strongly constrained by the symmetry and scaling properties of the theory. Based on this general…
We study properties of inner and outer functions in the Hardy space of the quaternionic unit ball. In particular, we give sufficient conditions as well as necessary ones for functions to be inner or outer.
We propose a Wigner quasiprobability distribution function for Hamiltonian systems in spaces of constant curvature --in this paper on hyperboloids--, which returns the correct marginals and has the covariance of the Shapiro functions under…
The Wigner function formalism has been applied to the analysis of elastic scattering processes. The new element of known formalism is the choice of the phase space on which the Wigner function is defined. This phase space is 4-dimensional…
A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…
We show that the behaviour in phase space of the Wigner function associated to the electromagnetic modes carries the information of both, the entanglement properties between matter and field, and the regions in parameter space where quantum…
General molecular dynamic approach, making possible direct calculation of eigen values and eigen functions for a quantum-mechanical system of an arbitrary symmetry is proposed. The method is based on analogy between discrete representation…
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…
The framework of Wigner functions for the canonical pair angle and orbital angular momentum, derived and analyzed in 2 recent papers [H. A. Kastrup, Phys.Rev. A 94, 062113(2016) and Phys.Rev. A 95, 052111(2017)] is applied to elementary…
In the present paper a method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. Starting with the problem of a reflection from an impenetrable wall, the obtained solution is then…
We derive simple formulas connecting the generalized Wigner functions for $s$-ordering with the density matrix, and vice-versa. These formulas proved very useful for quantum mechanical applications, as, for example, for connecting master…
We construct general Wigner rotations for both massive and massless particles in $D$-dimensional spacetime. We work out the explicit expressions of these Wigner rotations for arbitrary Lorentz transformations. We study the relation between…
Newly introduced equilibrium Wigner functions for particles with spin one-half are used in the semi-classical kinetic equations to study a possible relation between thermal vorticity and spin polarization. It is shown that in global…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
We introduce a notion of positive definiteness for functions $f\!:P\to\mathbb{R}$ defined on meet semilattices $(P,\preceq,\wedge)$ and prove several properties for these functions. In addition, we utilize the $LDL^{\rm T}$ decomposition of…
A lattice gauge theory with an action polynomial in independent field variables is considered. The link variables are described by unconstrained complex matrices instead of unitary ones. A mechanism which permits to switch off in the…
With the goal in mind of deriving a method to compute quantum corrections for the real-time evolution in quantum field theory, we analyze the problem from the perspective of the Wigner function. We argue that this provides the most natural…
Lattice Green functions appear in lattice gauge theories, in lattice models of statistical physics and in random walks. Here, space coordinates are treated as parameters and series expansions in the mass are obtained. The singular points in…