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 …

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 …

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 …

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 …

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 …

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 Page 1 Infinite Dimensional Analysis, Quantum
Probability and Related Topics Vol. 15, No. 2 (2012) 1250012 (8 pages) c World Scientific …

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 …

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 …