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Table of contents (3 chapters)
Keywords
About this book
"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
"This is an excellent volume which will be a valuable companion both for 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
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 communication relations or, equivalently, the uncertainty principle.
Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields.
Quantum dynamical semigroups as well as classical Markov semigroups are realized 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.
Reviews
"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
"This is an excellent volume which will be a valuable companion both for 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
Authors and Affiliations
Bibliographic Information
Book Title: An Introduction to Quantum Stochastic Calculus
Authors: K. R. Parthasarathy
Series Title: Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-8641-3
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Springer Basel AG 1992
Softcover ISBN: 978-3-0348-9711-2Published: 28 September 2012
eBook ISBN: 978-3-0348-8641-3Published: 06 December 2012
Series ISSN: 1017-0480
Series E-ISSN: 2296-4886
Edition Number: 1
Number of Pages: XI, 292