The accuracy of two widely used scalar relativistic Hartree-Fock pseudopotentials, the Trail-Needs-Dirac-Fock (TNDF) and the Burkatzki-Filippi-Dolg (BFD) pseudopotentials, is assessed. The performance of the pseudopotentials is tested for a chemically representative set of 34 first-row molecules. All comparisons are made at the Hartree-Fock level of theory, and both sets of pseudopotentials giv...

We show that under mild conditions, a Gaussian analytic function F that a.s. does not belong to a given weighted Bergman space or Bargmann–Fock space has the property that a.s. no non-zero function in that space vanishes where F does. This establishes a conjecture of Shapiro (1979) on Bergman spaces and allows us to resolve a question of Zhu (1993) on Bargmann–Fock spaces. We also give a simila...

It is shown that it is possible to construct an infinity of Fock spaces of flavor neutrinos depending on arbitrary unphysical mass parameters, in agreement with the theory of Blasone and Vitiello in the version proposed by Fujii, Habe and Yabuki. However, we show by reductio ad absurdum that these flavor neutrino Fock spaces are clever mathematical constructs without physical relevance, because...

Given a weighted ℓ 2 space with weights associated an entire function, we consider pairs of shift operators, whose commutators are diagonal when considered as operators over general Fock space. We establish calculus for the algebra these and apply it to case Gelfond–Leontiev derivatives. This class includes many known examples, such classic fractional derivatives Dunkl operators. allows us fram...

We construct a transformation between Bose Fock space Γ+ (h) and Fermi Fock space Γ − (h) that is super-symmetric in the sense that it converts Boson fields into Fermi fields over a fixed one-particle space h. The transformation involves the spectral splitting of h into a continuous direct integral of internal spaces (kω) ω . We intoduce a new theory of integration on the Fock spaces over L ( (...

The phase diagram of the Schwinger model on the lattice with one and two degenerate flavours of Wilson fermions is investigated in the Hartree-Fock approximation. In case of a single flavour (not directly amenable to numerical simulation), the calculation indicates the existence of the parity violating phase at both weak and intermediate-to-strong couplings. In the broken phase, the Hartree-Foc...

The phase diagram of the Schwinger model on the lattice with one and two degenerate flavours of Wilson fermions is investigated in the Hartree-Fock approximation. In case of a single flavour (not directly amenable to numerical simulation), the calculation indicates the existence of the parity violating phase at both weak and intermediate-to-strong couplings. In the broken phase, the Hartree-Foc...

The master field for a subclass of planar diagrams, so called rainbow diagrams, for higher dimensional large N theories is considered. An explicit representation for the master field in terms of noncommutative random variables in the modified interaction representation in the Boltzmannian Fock space is given. A natural interaction in the Boltzmannian Fock space is formulated by means of a ratio...

We consider the Fock-Sobolev space F p,m consisting of entire functions f such that f , the m-th order derivative of f , is in the Fock space F . We show that an entire function f is in F p,m if and only if the function zf(z) is in F . We also characterize the Carleson measures for the spaces F , establish the boundedness of the weighted Fock projection on appropriate L spaces, identify the Ban...

Bosons and fermions are described by using canonical generators of Cuntz algebras on any permutative representation. We show a fermionization of bosons which universally holds on any permutative representation of the Cuntz algebra O2. As examples, we show fermionizations on the Fock space and the infinite wedge. Mathematics Subject Classifications (2000). 46K10, 46L60