Quantum Stochastic Calculus and Representations of Lie Superalgebras
Eyre, Timothy M. W.
Quantum Stochastic Calculus and Representations of Lie Superalgebras [electronic resource] / by Timothy M. W. Eyre. - VIII, 148 p. online resource. - Lecture Notes in Mathematics, 1692 0075-8434 ; . - Lecture Notes in Mathematics, 1692 .
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.
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.
9783540683858
10.1007/BFb0096850 doi
Distribution (Probability theory.
Quantum theory.
Topological Groups.
Probability Theory and Stochastic Processes.
Quantum Information Technology, Spintronics.
Quantum Physics.
Topological Groups, Lie Groups.
QA273.A1-274.9 QA274-274.9
519.2
Quantum Stochastic Calculus and Representations of Lie Superalgebras [electronic resource] / by Timothy M. W. Eyre. - VIII, 148 p. online resource. - Lecture Notes in Mathematics, 1692 0075-8434 ; . - Lecture Notes in Mathematics, 1692 .
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.
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.
9783540683858
10.1007/BFb0096850 doi
Distribution (Probability theory.
Quantum theory.
Topological Groups.
Probability Theory and Stochastic Processes.
Quantum Information Technology, Spintronics.
Quantum Physics.
Topological Groups, Lie Groups.
QA273.A1-274.9 QA274-274.9
519.2