scholarly journals Compositions of states and observables in Fock spaces

2019 ◽  
Vol 32 (05) ◽  
pp. 2050012
Author(s):  
L. Amour ◽  
L. Jager ◽  
J. Nourrigat
Keyword(s):  
Quantum Electrodynamics ◽  
Fock Space ◽  
The Other ◽  
Wick Product ◽  
Fock Spaces ◽  
Weyl Symbol ◽  
Time Dynamics ◽  
Bargmann Transforms ◽  
Identification Operator

This article is concerned with compositions in the context of three standard quantizations in the framework of Fock spaces, namely, anti-Wick, Wick and Weyl quantizations. The first one is a composition of states also known as a Wick product and is closely related to the standard scattering identification operator encountered in Quantum Electrodynamics for issues on time dynamics (see [ 29 , 13 ]). Anti-Wick quantization and Segal–Bargmann transforms are implied here for that purpose. The other compositions are for observables (operators in some specific classes) for the Wick and Weyl symbols. For the Wick and Weyl symbols of the composition of two operators, we obtain an absolutely converging series and for the Weyl symbol, the remainder terms up to any orders of the expansion are controlled, still in the Fock space framework.

scholarly journals Factorization of the canonical bases for higher-level Fock spaces

2011 ◽  
Vol 55 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Susumu Ariki ◽  
Nicolas Jacon ◽  
Cédric Lecouvey
Keyword(s):  
Fock Space ◽  
Fock Spaces ◽  
Transition Matrices ◽  
Canonical Bases ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Graphic Module ◽  
Module Structures ◽  
Weight Modules

AbstractThe level l Fock space admits canonical bases $\mathcal{G}_{e}$ and $\smash{\mathcal{G}_{\infty}}$. They correspond to $\smash{\mathcal{U}_{v}(\widehat{\mathfrak{sl}}_{e})}$ and $\mathcal{U}_{v}({\mathfrak{sl}}_{\infty})$-module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in ℕ[v]. Restriction to the highest-weight modules generated by the empty l-partition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to Ariki–Koike algebras.

scholarly journals Interacting Fock spaces and subproduct systems

2020 ◽  
Vol 23 (03) ◽  
pp. 2050017
Author(s):  
Malte Gerhold ◽  
Michael Skeide
Keyword(s):  
Selfadjoint Operator ◽  
Operator Algebras ◽  
Fock Space ◽  
Fock Spaces ◽  
Full Generality ◽  
Necessary And Sufficient Criteria ◽  
Definition Of ◽  
Interacting Fock Space ◽  
Necessary And Sufficient

We present a new more flexible definition of interacting Fock space that allows to resolve in full generality the problem of embeddability. We show that the same is not possible for regularity. We apply embeddability to classify interacting Fock spaces by squeezings. We give necessary and sufficient criteria for when an interacting Fock space has only bounded creators, giving thus rise to new classes of non-selfadjoint and selfadjoint operator algebras.

scholarly journals Deformed Fock spaces, Hecke operators and monotone Fock space of Muraki

2012 ◽  
Vol 45 (2) ◽  
Author(s):  
Marek Bożejko
Keyword(s):  
Fock Space ◽  
Hecke Operators ◽  
Fock Spaces

AbstractThe main purpose of this paper is to extend our previous construction of

Retardation in non-dispersive interactions between molecules

1966 ◽  
Vol 295 (1443) ◽  
pp. 476-489 ◽  
Keyword(s):  
Quantum Electrodynamics ◽  
Exchange Interactions ◽  
Dipole Interaction ◽  
Second Order ◽  
The Other ◽  
Spin Orbit ◽  
Wave Zone ◽  
Expectation Value ◽  
Near Zone ◽  
The Matrix

The second order T matrix corresponding to the interaction between two molecules is calculated by quantum electrodynamics. In the near zone the matrix reduces to the expectation value of the Breit Hamiltonian for the two-centre problem. In the wave zone a retarded Briet operator is found for exchange interactions. A reduction to the Pauli limit is made. The interactions are discussed severally for the spin-spin, (spin-dipole)-(spin-dipole), spin-orbit and dipole-(spin-dipole) cases. At large separations the T matrix is complex and the imaginary parts, previously given for the dipole-dipole interaction, are found for the other cases.

scholarly journals PARAFERMIONS, PARABOSONS AND REPRESENTATIONS OF 𝔰𝔬(∞) AND 𝔬𝔰𝔭(1|∞)

2009 ◽  
Vol 20 (06) ◽  
pp. 693-715 ◽  
Author(s):  
N. I. STOILOVA ◽  
J. VAN DER JEUGT
Keyword(s):  
Lie Algebra ◽  
Fock Space ◽  
Complete Solution ◽  
Lie Superalgebra ◽  
Explicit Construction ◽  
Fock Spaces ◽  
Infinite Rank ◽  
Infinite Set ◽  
Basis Vectors

The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra 𝔰𝔬(∞) and of the Lie superalgebra 𝔬𝔰𝔭(1|∞). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labelled by certain infinite but stable Gelfand–Zetlin patterns, and the transformation of the basis is given explicitly. We also present expressions for the character of the Fock space representations.

scholarly journals Wavelet transforms in generalized Fock spaces

1997 ◽  
Vol 20 (4) ◽  
pp. 657-672 ◽  
Author(s):  
John Schmeelk ◽  
Arpad Takaci
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Fock Space ◽  
Generalized Function ◽  
Fock Spaces ◽  
The Individual ◽  
Individual Entry

A generalized Fock space is introduced as it was developed by Schmeelk [1-5], also Schmeelk and Takači [6-8]. The wavelet transform is then extended to this generalized Fock space. Since each component of a generalized Fock functional is a generalized function, the wavelet transform acts upon the individual entry much the same as was developed by Mikusinski and Mort [9] based upon earlier work of Mikusinski and Taylor [10]. It is then shown that the generalized wavelet transform applied to a member of our generalized Fock space produces a more appropriate functional for certain appfications.

scholarly journals LOCAL EXPONENTS AND INFINITESIMAL GENERATORS OF CANONICAL TRANSFORMATIONS ON BOSON FOCK SPACES

2004 ◽  
Vol 07 (04) ◽  
pp. 547-571 ◽  
Author(s):  
F. HIROSHIMA ◽  
K. R. ITO
Keyword(s):  
Canonical Transformation ◽  
Symplectic Group ◽  
Unitary Operator ◽  
Fock Space ◽  
Adjoint Operator ◽  
The Self ◽  
Canonical Transformations ◽  
Fock Spaces ◽  
Infinitesimal Generators ◽  
Boson Fock Space

A one-parameter symplectic group {etÂ}t∈ℝ derives proper canonical transformations indexed by t on a Boson–Fock space. It has been known that the unitary operator Ut implementing such a proper canonical transformation gives a projective unitary representation of {etÂ}t∈ℝ on the Boson–Fock space and that Ut can be expressed as a normal-ordered form. We rigorously derive the self-adjoint operator Δ(Â) and a local exponent [Formula: see text] with a real-valued function τÂ(·) such that [Formula: see text].

scholarly journals Fourier transforms in generalized Fock spaces

1990 ◽  
Vol 13 (3) ◽  
pp. 431-441
Author(s):  
John Schmeelk
Keyword(s):  
Fourier Transform ◽  
Taylor Series ◽  
Fourier Transforms ◽  
Fock Space ◽  
Natural Generalization ◽  
Fock Spaces ◽  
Test Functions ◽  
Tempered Distributions ◽  
Tempered Distribution ◽  
The Fourier Transform

A classical Fock space consists of functions of the form,Φ↔(ϕ0,ϕ1,…,ϕq,…),whereϕ0∈Candϕq∈L2(R3q),q≥1. We will replace theϕq,q≥1withq-symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter,s, which sweeps out a scale of generalized Fock spaces.

scholarly journals Relativistic density-functional theory based on effective quantum electrodynamics

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Julien Toulouse
Keyword(s):  
Density Functional Theory ◽  
Quantum Electrodynamics ◽  
Density Functional ◽  
Degrees Of Freedom ◽  
Fock Space ◽  
Particle Interaction ◽  
Functional Theory ◽  
Electron Positron ◽  
Molecular Calculations ◽  
Coordinate Scaling

A relativistic density-functional theory based on a Fock-space effective quantum-electrodynamics (QED) Hamiltonian using the Coulomb or Coulomb-Breit two-particle interaction is developed. This effective QED theory properly includes the effects of vacuum polarization through the creation of electron-positron pairs but does not include explicitly the photon degrees of freedom. It is thus a more tractable alternative to full QED for atomic and molecular calculations. Using the constrained-search formalism, a Kohn-Sham scheme is formulated in a quite similar way to non-relativistic density-functional theory, and some exact properties of the involved density functionals are studied, namely charge-conjugation symmetry and uniform coordinate scaling. The usual no-pair Kohn-Sham scheme is obtained as a well-defined approximation to this relativistic density-functional theory.

scholarly journals Toeplitz Operators with I M O s Symbols between Generalized Fock Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yiyuan Zhang ◽  
Guangfu Cao ◽  
Li He
Keyword(s):  
Toeplitz Operators ◽  
Fock Space ◽  
Fock Spaces

In this paper, we study the mapping properties of Toeplitz operators T f associated with IMO s   symbols f acting between two generalized Fock spaces F φ p , where 1 < s ≤ ∞ . We characterize bounded or compact Toeplitz operators T f from one generalized Fock space F φ p to another F φ q , respectively, in four cases.

Sign in / Sign up

Export Citation Format

Share Document