scholarly journals Segal-Bargmann transforms of one-mode interacting Fock spaces associated with Gaussian and Poisson measures

2002 ◽  
Vol 131 (3) ◽  
pp. 815-823 ◽  
Author(s):  
Nobuhiro Asai ◽  
Izumi Kubo ◽  
Hui-Hsiung Kuo
Keyword(s):  
Fock Spaces ◽  
Bargmann Transforms ◽  
Poisson Measures

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.

Non-trivial 1d and 2d Segal–Bargmann transforms

2019 ◽  
Vol 30 (7) ◽  
pp. 547-563 ◽  
Author(s):  
Abdelhadi Benahmadi ◽  
Allal Ghanmi
Keyword(s):  
Bargmann Transforms

On improvements of the order of approximation in the Poisson limit theorem

1996 ◽  
Vol 33 (01) ◽  
pp. 146-155 ◽  
Author(s):  
K. Borovkov ◽  
D. Pfeifer
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Poisson Approximation ◽  
Order Of Approximation ◽  
Operator Semigroups ◽  
Bernoulli Random Variables ◽  
Usual Rate ◽  
Poisson Limit ◽  
Poisson Measures ◽  
Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

Asymptotic Expansions in the Exponent: a Compound Poisson Approach

1997 ◽  
Vol 29 (02) ◽  
pp. 374-387 ◽  
Author(s):  
V. Čekanavičius
Keyword(s):  
Asymptotic Expansion ◽  
Large Deviations ◽  
Poisson Distribution ◽  
Asymptotic Expansions ◽  
Compound Poisson ◽  
Poisson Measures ◽  
Poisson Approximations

The accuracy of the Normal or Poisson approximations can be significantly improved by adding part of an asymptotic expansion in the exponent. The signed-compound-Poisson measures obtained in this manner can be of the same structure as the Poisson distribution. For large deviations we prove that signed-compound-Poisson measures enlarge the zone of equivalence for tails.

scholarly journals Factorization and reflexivity on Fock spaces

1995 ◽  
Vol 23 (3) ◽  
pp. 268-286 ◽  
Author(s):  
Alvaro Arias ◽  
Gelu Popescu
Keyword(s):  
Fock Spaces

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.

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