Abstract.
In quantum stochastic calculus on the symmetric Fock space over L 2(ℝ+), adapted processes of operators are integrated with respect to creation, annihilation and number processes. The main property which allows this integration is that the increments of integrators between s and t act only on Fock space over L 2([s, t]). In this article, we prove that there are no other process of closable operators on coherent vectors with this property. Thus the only possible integrators in quantum stochastic calculus are the creation, annihilation and number processes.
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Received: 7 June 1999 / Revised version: 27 December 1999 / Published online: 12 October 2000
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Coquio, A. Why are there only three quantum noises?. Probab Theory Relat Fields 118, 349–364 (2000). https://doi.org/10.1007/PL00008746
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DOI: https://doi.org/10.1007/PL00008746