Abstract
A rigorous mathematical formulation of higher powers of quantum white noises is given on the basis of the most recent theory of white noise distributions due to Cochran, Kuo and Sengupta. The renormalized quantum Itô formula due to Accardi, Lu and Volovich is derived from the renormalized product formula based on integral kernel operators on white noise functions. During the discussion, the analytic characterization of operator symbols and the expansion theorem for a white noise operator in terms of integral kernel operators are established.
| Original language | English |
|---|---|
| Pages (from-to) | 533-559 |
| Number of pages | 27 |
| Journal | Infinite Dimensional Analysis, Quantum Probability and Related Topics |
| Volume | 1 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1998 Oct |
| Externally published | Yes |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Mathematical Physics
- Applied Mathematics