Related papers: Pseudodifferential Weyl calculus on vector bundles

We study discrete spectrum of self-adjoint Weyl pseudodifferential operators with discontinuous symbols of the form $1_\Omega \phi$ where $1_\Omega$ is the indicator of a domain in $\Omega\subset\mathbb R^2$, and $\phi\in C^\infty_0(\mathbb…

We give a geometric proof of a theorem of Weyl on the continuous part of the spectrum of Sturm-Liouville operators on the half-line with asymptotically constant coefficients. Earlier proofs due to Weyl and Kodaira depend on special features…

We study pseudodifferential operators associated to microlocally defined normed symbol spaces of limited regularity, introduced by J. Sj\"ostrand. Boundedness of such operators on modulation spaces is obtained under suitable conditions, and…

We study the geometry and topology of (filtered) algebra-bundles ${\bf\Psi}^{\mathbb Z}$ over a smooth manifold $X$ with typical fibre $\Psi^{\mathbb Z}(Z; V)$, the algebra of classical pseudodifferential operators of integral order on the…

We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given…

We study a class of quadratic time-frequency representations that, roughly speaking, are obtained by linear perturbations of the Wigner transform. They satisfy Moyal's formula by default and share many other properties with the Wigner…

A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…

In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We particularise to this group our general construction [4,3,2] of pseudo-differential calculi on graded groups. The relation between the Weyl…

We consider global pseudodifferential operators on symmetric spaces of noncompact type, defined using spherical functions. The associated symbols have a natural probabilistic form that extend the notion of the characteristic exponent…

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…

In the objective of studying concentration and oscillation properties of eigenfunctions of the discrete Laplacian on regular graphs, we construct a pseudo-differential calculus on homogeneous trees, their universal covers. We define symbol…

We derive a semi-classical nonequilibrium work identity by applying the Wigner-Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us, to the leading order in $\hbar$, to overcome the problem of…

In this work, we consider fixed $1/2$ spin particles interacting with the quantized radiation field in the context of quantum electrodynamics (QED). We investigate the time evolution operator in studying the reduced propagator (interaction…

We prove that the semi-classical Schrodinger operator with growing potential on a complete Riemannian manifold satisfies the Weyl law.

The Weyl principle is extended from the Riemannian to the pseudo-Riemannian setting, and subsequently to manifolds equipped with generic symmetric $(0,2)$-tensors. More precisely, we construct a family of generalized curvature measures…

Specific global symbol classes and corresponding pseudodifferential operators of infinite order that act continuously on the space of tempered ultradistributions of Beurling and Roumieu type are constructed. For these classes, symbolic…

We define an (equivariant) quaternionic analytic torsion for antiselfdual vector bundles on quaternionic Kaehler manifolds, using ideas by Leung and Yi. We compute this torsion for vector bundles on quaternionic homogeneous spaces with…

Invertible maps from operators of quantum obvservables onto functions of c-number arguments and their associative products are first assessed. Different types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution are…

The first part of the paper is devoted to the $G$-type spaces i.e. the spaces $G^\alpha_\alpha (\mathbb R^d_+)$, $\alpha\geq 1$ and their duals which can be described as analogous to the Gelfand-Shilov spaces and their duals but with…

The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum…