Self-adjointness and boundedness in quadratic quantization

Abstract

We construct a counter example showing, for the quadratic quantization, the identity $(\Gamma (T){)}^{\ast }=\Gamma (T^{\ast })$ is not necessarily true. We characterize all operators on the one-particle algebra whose quadratic quantization are self-adjoint operators on the quadratic Fock space. Finally, we discuss the boundedness of the quadratic quantization.

14 pages

References in corpus (3)

• Quadratic bosonic and free white noises
• The quadratic Fock functor
• Quadratic exponential vectors

Cited by in corpus (1)

• Quadratic Open Quantum Harmonic Oscillator