Related papers: Comments on the Weyl-Wigner calculus for lattice m…
The Weyl-Wigner formulation of quantum confined systems poses several interesting problems. The energy stargenvalue equation, as well as the dynamical equation does not display the expected solutions. In this paper we review some previous…
The phenomenon of unpaired Weyl fermions appearing on the sole 2n-dimensional boundary of a (2n+1)-dimensional manifold with massive Dirac fermions was recently analyzed in a companion paper by one of the authors. In this Letter we show…
The W-infinity minimal models are conformal field theories which can describe the edge excitations of the hierarchical plateaus in the quantum Hall effect. In this paper, these models are described in very explicit terms by using a bosonic…
A fluid analog of the information flux in the phase-space associated to purity and von Neumann entropy are identified in the Weyl-Wigner formalism of quantum mechanics. Once constrained by symmetry and positiveness, the encountered…
We propose a discrete lattice version of the Fokker-Planck kinetic equation along lines similar to the Lattice-Boltzmann scheme. Our work extends an earlier one-dimensional formulation to arbitrary spatial dimension $D$. A generalized…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems.…
Developments in algorithms over the past decade suggest that there is a new computational approach to a class of quantum field theories. This approach is based on rewriting the partition function in a representation similar to the…
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static…
Simulations in compact U(1) lattice gauge theory in 4D show now beyond any reasonable doubts that the phase transition separating the Coulomb from the confined phase is of first order, albeit a very weak one. This settles the issue from the…
In two-dimensional space a subtle point that for the case of both space-space and momentum-momentum noncommuting, different from the case of only space-space noncommuting, the deformed Heisenberg-Weyl algebra in noncommutative space is not…
A new pseudoclassical model to describe Weyl particles is proposed. Different ways of its quantization are presented. They all lead to the theory of Weyl particle; namely, the massless Dirac equation and the Weyl condition are reproduced.…
In this paper, we address the phase space formulation of the Jaynes-Cummings model through the explicit construction of the full Wigner function for a hybrid bipartite quantum system composed of a two-level atom and a quantized coherent…
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the…
Classical model of light in helicity formalism is presented. Then quantum point of view at photons -- construction and interpretation of photon wave function is proposed. Quantum mechanics of photon is investigated. The Bia\l ynicki --…
In various dimensional Euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In $8n$ and $1+8n$ dimensions, we find a difficulty to…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…
We consider quantum phase-space dynamics using Wigner's representation of quantum mechanics. We stress the usefulness of the integral form for the description of Wigner's phase-space current~$\bm J$ as an alternative to the popular Moyal…