We introduce a new formalism of differential operators for a general associative algebra A. It replaces Grothendieck’s notion of differential operator on a commutative algebra in such a way that derivations of the commutative algebra are replaced by DerA, the bimodule of double derivations. Our differential operators act not on the algebra A itself but rather on F(A), a certain ‘Fock space’ ass...

We compute the Dixmier trace of pseudo-Toeplitz operators on the Fock space. As an application we find a formula for the Dixmier trace of the product of commutators of Toeplitz operators on the Hardy and weighted Bergman spaces on the unit ball of C. This generalizes an earlier work of Helton-Howe for the usual trace of the anti-symmetrization of Toeplitz operators.

We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in L2(e−2φ) where φ is a subharmonic function with ∆φ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous CauchyRiemann equation and we characterize the compactness of this operator in terms of ∆φ.

We obtain new and simple characterizations for the boundedness and compactness of weighted composition operators on the Fock space over C. We also describe all weighted composition operators that are normal or isometric.

We construct a vertex operator realization for the simple current primary fields of WZW theories which are based on simply laced affine Lie algebras g. This is achieved by employing an embedding of the integrable highest weight modules of g into the Fock space for a bosonic string compactified on the weight lattice of g. Our vertex operators are universal in the sense that a single expression f...

Hartree-Fock calculations with the SKX Skyrme interaction are carried out to obtain a-decay Q values for deformed nuclei above Pb assuming axial symmetry. The results for even-even nuclei are compared with the experiment and with the previous calculations. Predictions are made for a-decay Q values and half-lives of even-even superheavy nuclei. The results are also compared for the recently disc...

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für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

We construct the exchange gate with small elementary gates on the space of qudits, which consist of three controlled shift gates and three ”reverse” gates. This is a natural extension of the qubit case. We also consider a similar subject on the Fock space, but in this case it is not clear what elementary gates are. We present some related problems.