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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Quantum Stochastic Processes and Noncommutative Geometry (Hardcover)
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Quantum Stochastic Processes and Noncommutative Geometry (Hardcover)
Series: Cambridge Tracts in Mathematics
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The classical theory of stochastic processes has important
applications arising from the need to describe irreversible
evolutions in classical mechanics; analogously quantum stochastic
processes can be used to model the dynamics of irreversible quantum
systems. Noncommutative, i.e. quantum, geometry provides a
framework in which quantum stochastic structures can be explored.
This book is the first to describe how these two mathematical
constructions are related. In particular, key ideas of semigroups
and complete positivity are combined to yield quantum dynamical
semigroups (QDS). Sinha and Goswami also develop a general theory
of Evans-Hudson dilation for both bounded and unbounded
coefficients. The unique features of the book, including the
interaction of QDS and quantum stochastic calculus with
noncommutative geometry and a thorough discussion of this calculus
with unbounded coefficients, will make it of interest to graduate
students and researchers in functional analysis, probability and
mathematical physics.
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