Monographs in Mathematics

An Introduction to Quantum Stochastic Calculus

Authors: Parthasarathy, K.R.

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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   


Table of contents (3 chapters)

  • Events, Observables and States

    Parthasarathy, K. R.

    Pages 1-89

  • Observables and States in Tensor Products of Hilbert Spaces

    Parthasarathy, K. R.

    Pages 91-177

  • Stochastic Integration and Quantum Ito’s Formula

    Parthasarathy, K. R.

    Pages 179-273

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0348-8641-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-0348-9711-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Quantum Stochastic Calculus
Authors
Series Title
Monographs in Mathematics
Series Volume
85
Copyright
1992
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8641-3
DOI
10.1007/978-3-0348-8641-3
Softcover ISBN
978-3-0348-9711-2
Series ISSN
1017-0480
Edition Number
1
Number of Pages
XI, 292
Topics