"An Introduction to Quantum Stochastic Calculus" aims to deepen
our understanding of the dynamics of systems subject to the laws of
chance both from the classical and the quantum points of view and
stimulate further research in their unification. This is probably
the first systematic attempt to weave classical probability theory
into the quantum framework and provides a wealth of interesting
features:
The origin of Ito s correction formulae for Brownian motion and the
Poisson process can be traced to commutation relations or,
equivalently, the uncertainty principle.
Quantum stochastic integration enables the possibility of seeing
new relationships between fermion and boson fields.
Many quantum dynamical semigroups as well as classical Markov
semigroups are realised through unitary operator evolutions.
The text is almost self-contained and requires only an elementary
knowledge of operator theory and probability theory at the graduate
level.
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"This is an excellent volume which will be a valuable companion
bothto those who are already active in the field and those who are
new to it. Furthermore there are a large number of stimulating
exercises scattered through the text which will be invaluable to
students."
(Mathematical Reviews)
"This monograph gives a systematic and self-contained introduction
to the Fock space quantum stochastic calculus in its basic form
(...) by making emphasis on the mathematical aspects of quantum
formalism and its connections with classical probability and by
extensive presentation of carefully selected functional analytic
material. This makes the book very convenient for a reader with the
probability-theoretic orientation, wishing to make acquaintance
with wonders of the noncommutative probability, and, more
specifcally, for a mathematics student studying this field."
(Zentralblatt MATH)
"Elegantly written, with obvious appreciation for fine points of
higher mathematics (...) most notable is the] author's effort to
weave classical probability theory into a] quantum framework.
"(The American Mathematical Monthly)
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