Skip to content

Online ordering will be unavailable on Saturday 10 December 2022, 0800-1800 GMT.

To place an order, please contact Customer Services.

UK/ROW +44 (0) 1223 326050 | US 1 800 872 7423 or 1 212 337 5000 | Australia/New Zealand 61 3 86711400 or 1800 005 210, New Zealand 0800 023 520

Register Sign in Wishlist
Quantum Stochastic Processes and Noncommutative Geometry

Quantum Stochastic Processes and Noncommutative Geometry


Part of Cambridge Tracts in Mathematics

  • Date Published: January 2007
  • availability: In stock
  • format: Hardback
  • isbn: 9780521834506


Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • 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.

    • This book is the first to describe how the mathematical constructions of noncommutative geometry and quantum stochastic structures are related
    • Contains many unique features, e.g. discussion of calculus with unbounded operator coefficients
    • Accessible to a wide range of graduate students and researchers
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: January 2007
    • format: Hardback
    • isbn: 9780521834506
    • length: 300 pages
    • dimensions: 235 x 162 x 20 mm
    • weight: 0.561kg
    • availability: In stock
  • Table of Contents

    1. Introduction
    2. Preliminaries
    3. Quantum dynamical semigroups
    4. Hilbert modules
    5. Quantum stochastic calculus with bounded coefficients
    6. Dilation of quantum dynamical semigroups with bounded generator
    7. Quantum stochastic calculus with unbounded coefficients
    8. Dilation of quantum dynamical semigroups with unbounded generator
    9. Noncommutative geometry and quantum stochastic processes

  • Authors

    Kalyan B. Sinha, Indian Statistical Institute, New Delhi
    Kalyan Sinha is a Distinguished Scientist in the Statistics-Mathematics Unit at the Indian Statistical Institute, New Dehli.

    Debashish Goswami, Indian Statistical Institute, Kolkata
    Debashish Goswami is an Assistant Professor in the Statistics-Mathematics Unit at the Indian Statistical Institute, Kolkata.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.