## Abstract

A rigged Hilbert space formalism is introduced to study Fock space operators. The symbols of continuous operators on a rigged Fock space are characterized in terms of Bargmann-Segal spaces and complex Gaussian integrals. In particular, characterizations of bounded operators and of operators of Hilbert-Schmidt class on the middle Fock space are obtained. As an application we establish an operator version of chaotic expansion (Wiener-Itô expansion) and describe a relation to the Fock expansion in terms of the Wick exponential of the number operator. As another application we discuss regularity property of a solution to a normal-ordered white noise differential equation generalizing a quantum stochastic differential equation.

Original language | English |
---|---|

Pages (from-to) | 311-338 |

Number of pages | 28 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 56 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2004 |

## Keywords

- Bargmann-Segal space
- Chaotic expansion
- Fock space
- Gaussian analysis
- Integral kernel operator
- Operator symbol
- Quantum stochastic differential equation
- White noise differential equation