Related papers: Electronic Fock space as associative superalgebra
A general theorem due to Howe of dual action of a classical group and a certain non-associative algebra on a space of symmetric or alternating tensors is reformulated in a setting of second quantization, and familiar examples in atomic and…
Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view. To this end an alternative technique of quantization outlined by the authors in a previous work and that is based in…
The subject of this paper are operators represented on a Fock space which act only on the two leading components of the tensor. We unify the constructions from arXiv:math/0702158, arXiv:0709.4334, arXiv:0812.0895, and arXiv:1003.2998, and…
This paper discusses quantum mechanical schemas for describing waves with non-abelian phases, Fock spaces of annihilation-creation operators for these structures, and the Feynman recipe for obtaining descriptions of particle interactions…
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ``infinite'', Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot…
General properties of new models of the electronic Fock spaces based on the notion of (p,q)-sheaves are studied. Interrelation between simple sheaves and density operators is established. Explicit expressions for the transformed reduced…
We give explicit descriptions of all path connected components and isolated points of both spaces of composition operators and nonzero weighted composition operators acting from a Fock space $\mathcal{F}^p(\mathbb{C}^n)$ to another one…
A formula is written down for the annhilation operator(bose or fermi) in terms of the corresponding observable bilinears namely currents and densities. The Fock space representation of these formulas is clarified. A conjecture is written…
A categorical axiomatic theory of creation/annihilation operators on bosonic Fock space is introduced and the combinatorial model that motivated it is presented. Commutation relations and coherent states are considered in both frameworks.
We study certain densely defined unbounded operators on the Fock space. These are the annihilation and creation operators of quantum mechanics. In several complex variables we have the $\partial$-operator and its adjoint $\partial^*$ acting…
Modern challenges arising in the fields of theoretical and experimental physics require new powerful tools for high-precision electronic structure modelling; one of the most perspective tools is the relativistic Fock space coupled cluster…
We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard…
We present a reduced density operator for electronically open molecules by explicitly averaging over the environmental degrees of freedom of the composite Hamiltonian. Specifically, we include the particle-number non-conserving…
A Fock space is introduced that admits an action of a quantum group of type A supplemented with some extra operators. The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimenisonal…
We perform a global analysis of the experimental data of the electromagnetic nucleon form factors, in space-like and time-like regions. We give the expressions of the observables in annihilation processes, such as $p+\bar{p}\to \ell^+…
This chapter discusses contemporary quantum chemical methods and provides general insights into modern electronic structure theory with a focus on heavy-element-containing compounds. We first give a short overview of relativistic…
We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum…
Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined to the extent that the question of whether weighted composition operators on…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…