Quadratic exponential vectors

TL;DR

This paper establishes conditions for the existence and properties of quadratic exponential vectors in quadratic Fock space, including their linear independence, totality, and scalar product formulas for a broader class of functions.

Contribution

It provides new existence criteria, proves linear independence and totality, and extends scalar product formulas for quadratic exponential vectors in Fock space.

Findings

Established sufficient conditions for existence of quadratic exponential vectors.

Proved linear independence and totality of these vectors.

Extended scalar product formulas to a broader class of test functions.

Abstract

We give a sufficient condition for the existence of a quadratic exponential vector with test function in L2(Rd) ? L?(Rd). We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique different from the one used, we also extend, to a more general class of test functions, the explicit form of the scalar product between two such vectors.