Overview
- One of the first systematic attempts to weave classical probability theory into the quantum framework
- Self-contained introduction to the Fock space quantum stochastic calculus in its basic form
- A large number of stimulating exercises make the text invaluable to students?
- Includes supplementary material: sn.pub/extras
Part of the book series: Modern Birkhäuser Classics (MBC)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (3 chapters)
Keywords
- Fock space
- noncommutative probability
- quantum Ito’s product formula
- quantum dynamical semigroup
- quantum stochastic differential equations
- stochastic integration
- Brownian motion
- calculus
- differential equation
- Hilbert space
- integration
- operator
- operator theory
- Poisson process
- probability
- probability theory
- stochastic calculus
- stochastic differential equation
- tensor
About this book
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.
- - -
This is an excellent volume which will be a valuable companion both to 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, withobvious 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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: An Introduction to Quantum Stochastic Calculus
Authors: K.R. Parthasarathy
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-3-0348-0566-7
Publisher: Birkhäuser Basel
-
eBook Packages: Springer Book Archive
Copyright Information: Springer Basel 1992
Softcover ISBN: 978-3-0348-0565-0Published: 14 December 2012
eBook ISBN: 978-3-0348-0566-7Published: 13 December 2012
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: XI, 290
Additional Information: Originally published as volume 85 in the Monographs in Mathematics series
Topics: Probability Theory and Stochastic Processes, Mathematical Physics, Functional Analysis, Operator Theory