Quantum Stochastic Calculus and Representations of Lie Superalgebras

1. Auflage 1998
ISBN: 978-3-540-64897-0
Verlag: Springer

Buch, Englisch, Band 1692, 148 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 248 g

Reihe: Lecture Notes in Mathematics

This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic 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 stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.

Zielgruppe

Research

Autoren/Hrsg.

Eyre, Timothy M.W.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

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