We give a necessary and sufficient condition for the existence of a quadratic exponential vector with test function in $L^2(\mathbb{R}^d)\cap L^\infty(\mathbb{R}^d)$. We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique different from the one used in \cite {ADS}, we also extend, to a more general class of test functions, the explicit form of the scalar product between two such vectors.
Accardi, L., Dhahri, A. (2009). Quadratic exponential vectors. JOURNAL OF MATHEMATICAL PHYSICS, 50(12), 122103.
Quadratic exponential vectors
ACCARDI, LUIGI;
2009-01-01
Abstract
We give a necessary and sufficient condition for the existence of a quadratic exponential vector with test function in $L^2(\mathbb{R}^d)\cap L^\infty(\mathbb{R}^d)$. We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique different from the one used in \cite {ADS}, we also extend, to a more general class of test functions, the explicit form of the scalar product between two such vectors.File in questo prodotto:
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