Related papers: Precise Wigner-Weyl calculus for lattice models
A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented, with special emphasis in the implications of rotational periodicity and angular-momentum discreteness.
Building on the many existing algorithms for calculating the DC transport properties of quantum tight-binding models, we develop a systematic approach that expresses finite frequency observables in terms of the stationary Green's function…
Lattice walks are used to model various physical phenomena. In particular, walks within Weyl chambers connect directly to representation theory via the Littelmann path model. We derive asymptotics for centrally weighted lattice walks within…
Starting from the quantum Liouville equation for the density operator and applying the Weyl quantization, Wigner equations for the longitudinal and transversal optical and acoustic phonons are deduced. The equations are valid for any solid,…
We revisit the calculation of gravitational radiation through the use of Weyl scalars. We point out several possible problems arising from gauge and tetrad ambiguities and ways to address them. Our analysis indicates how, relatively simple…
We develop our earlier approach to the Weyl calculus for representations of infinite-dimensional Lie groups by establishing continuity properties of the Moyal product for symbols belonging to various modulation spaces. For instance, we…
The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…
We present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. When a certain commutative subalgebra is finitely generated over an algebraically closed field we obtain a classification…
We study a system of electrons on a one-dimensional lattice, interacting through the long range Coulomb forces, by means of a variational technique which is the strong coupling analog of the Gutzwiller approach. The problem is thus the…
The Weyl-Wigner-Moyal formalism is developed for spin by means of a correspondence between spherical harmonics and spherical harmonic tensor operators. The analogue of the Moyal expansion is developed for the Weyl symbol of the product of…
A new method for the construction of conformally invariant equations in an arbitrary four dimensional (pseudo-) Riemannian space is presented. This method uses the Weyl geometry as a tool and exploits the natural conformal invariance we can…
This paper presents the detailed, standard treatment of a simple, gauge invariant action for Weyl and Weyl-like Cartan geometries outlined in a previous paper. In addition to the familiar scalar curvature squared and Maxwell terms, the…
We introduce a new Weyl-invariant and generally-covariant vector-tensor theory with higher derivatives. This theory can be induced by extending the mimetic construction to vector fields of conformal weight four. We demonstrate that in…
We describe boundedness and compactness properties for the operators obtained by the Weyl-Pedersen calculus in the case of the irreducible unitary representations of nilpotent Lie groups that are associated with flat coadjoint orbits. We…
We give a complete picture of when the tensor product of an induced module and a Weyl module is a tilting module for the algebraic group $SL_2$ over an algebraically closed field of characteristic $p$. Whilst the result is recursive by…
The single graphene layer is a novel material consisting of a flat monolayer of carbon atoms packed in a two-dimensional honeycomb-lattice, in which the electron dynamics is governed by the Dirac equation. A pseudo-spin phase-space approach…
Applying a Weyl-Stratonovich transform to the evolution equation of the Wigner function in an electromagnetic field yields a multidimensional gauge-invariant equation which is numerically very challenging to solve. In this work, we apply…
The vertex algebra W_{1+\infty,c} with central charge c may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integer n\geq 1, it was conjectured in the physics…
The Weyl-Wigner-Moyal formalism for quantum particle with discrete internal degrees of freedom is developed. A one to one correspondence between operators in the Hilbert space $L^{2}(\mathbb{R}^{3})\otimes{\mathcal{H}}^{(s+1)}$ and…
We study the twisted Weyl symbol of metaplectic operators; this requires the definition of an index for symplectic paths related to the Conley-Zehnder index. We thereafter define a metaplectically covariant algebra of pseudo-differential…