Quantum Stochastic Calculus and Representations of Lie Superalgebras / Edition 1

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This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum shastic calculus. Quantum shastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum shastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum shastic calculus and to provide a framework for future research into this new and fertile area.

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Product Details

  • ISBN-13: 9783540648970
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 10/30/1998
  • Series: Lecture Notes in Mathematics Series, #1692
  • Edition description: 1998
  • Edition number: 1
  • Pages: 144
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.34 (d)

Table of Contents

Quantum shastic calculus.- Z2-graded structures.- Representations of lie superalgebras in Z2-graded quantum shastic calculus.- The ungraded higher order Ito product formula.- The Ito superalgebra.- Some results in Z2-graded quantum shastic calculus.- Chaotic expansions.- Extensions.

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