Ji 教授のアブストラクト

In this paper, we construct the quadratic Fock space over a closed t-subalgebra of Hilbert Schmidt operators, providing a non-commutative generalization of the scalar renormalized square white noise model. We explicitly construct quadratic exponential vectors for trace class operators satisfying a specic trace norm bound, and by applying the quadratic exponential vectors, we derive the quadratic Wiener-Itô decomposition. Finally, we characterize when the quadratic second quantization of a bounded linear map is isometric in terms of properties of the bounded linear map. By applying a continuous extension of Wigner's theorem from real to complex Hilbert spaces, we prove that the quadratic second quantization extends to an isometry if and only if the underlying map preserves specic trace-moments, yielding a rigid structural representation implemented by a real isometry.