Quadratic fock space calculus (I): some results on quadratic creation and preservation operators

O Alzeley, H Rebei, H Rguigui - Quantum Information Processing, 2024 - Springer
This paper is a fundamental exploration of quantum theory within the quadratic Fock space
in consistency with the quadratic quantization program, with a particular focus on two sets of …

Identification of the one-mode quadratic Heisenberg group with the projective group and holomorphic representation

H Rebei, H Rguigui, A Riahi… - … , Quantum Probability and …, 2020 - World Scientific
In this paper, we provide a new reformulation of the quadratic analogue of the Weyl
relations. Especially, we offer some adjustments [10] on these relations and the …

The quadratic Fock functor

L Accardi, A Dhahri - Journal of mathematical physics, 2010 - pubs.aip.org
We construct the quadratic analog of the boson Fock functor. While in the first order (linear)
case all contractions on the 1-particle space can be second quantized, the semigroup of …

Quadratic exponential vectors

L Accardi, A Dhahri - Journal of mathematical physics, 2009 - pubs.aip.org
We give a necessary and sufficient condition for the existence of a quadratic exponential
vector with test function in L 2 (R d)∩ L∞(R d)⁠. We prove the linear independence and …

Quadratic Fock Space Calculus (II): Positivity of the Preservation Operator and Linear Independence of the Quadratic Exponential Vectors

O Alzeley, H Rebei, H Rguigui - Complex Analysis and Operator Theory, 2024 - Springer
It have been proved in Accardi and Dhahri (J Math Phys 51: 2, 2010) that the set of the
exponential vectors Φ (g), g∈ K:= L 2 (R d)∩ L∞(R d) associated with different test …

Self-adjointness and boundedness in quadratic quantization

A Dhahri - Journal of Mathematical Physics, 2014 - pubs.aip.org
We construct a counter example showing, for the quadratic quantization, the identity (Γ (T))*=
Γ (T*) is not necessarily true. We characterize all operators on the one-particle algebra …

On the quadratic Fock functor

A Dhahri - Infinite Dimensional Analysis, Quantum Probability and …, 2012 - World Scientific
ON THE QUADRATIC FOCK FUNCTOR Page 1 Infinite Dimensional Analysis, Quantum
Probability and Related Topics Vol. 15, No. 2 (2012) 1250012 (8 pages) c World Scientific …

[PDF][PDF] Emergence of Quantum Theories from Classical Probability: Historical Origins, Developments, and Open Problems

L Accardi, YG Lu - Journal of Stochastic Analysis, 2020 - repository.lsu.edu
After briefly mentioning some achievements of quantum probability during the past 20 years,
we concentrate our attention on the emergence of natural extensions of usual quantum …

[PDF][PDF] Journal of Stochastic Analysis

L Accardi, YG Lu - Emergence, 2020 - academia.edu
After briefly mentioning some achievements of quantum probability during the past 20 years,
we concentrate our attention on the emergence of natural extensions of usual quantum …