Infinite Dimensional Groups and Algebras in Quantum Physics

ISBN-13: 9783662140536 / Angielski / Miękka / 2013 / 218 str.

Johnny T. Ottesen

Opis

The idea of writing this book appeared when I was working on some problems related to representations of physically relevant infinite - mensional groups of operators on physically relevant Hilbert spaces. The considerations were local, reducing the subject to dealing with representations of infinite-dimensional Lie algebras associated with the associated groups. There is a large number of specialized articles and books on parts of this subject, but to our suprise only a few represent the point of view given in this book. Moreover, none of the written material was self-contained. At present, the subject has not reached its final form and active research is still being undertaken. I present this subject of growing importance in a unified manner and by a fairly simple approach. I present a route by which students can absorb and understand the subject, only assuming that the reader is familliar with functional analysis, especially bounded and unbounded operators on Hilbert spaces. Moreover, I assume a little basic knowledge of algebras , Lie algebras, Lie groups, and manifolds- at least the definitions. The contents are presented in detail in the introduction in Chap. The manuscript of this book has been succesfully used by some advanced graduate students at Aarhus University, Denmark, in their "A-exame'. I thank them for comments.

Spis treści

The Spin Representation of the Infinite—Dimensional Orthogonal Group.- The Metaplectic Representation of the Infinite-Dimensional Symplectic Group.- Loop Algebras and the Virasoro Algebra.- Applications.

O autorze

On the basis of classical representation theory and basic facts of functional analysis the author contructs the spin representations of the infinitesimal orthogonal group and the metaplectic representation of an infinite-dimensional symplectic group in a constructive novel approach. The text addresses graduate students and researchers.

Blurb

The representation theory of infinite-dimensional groups is an important tool for studying conformal field theory, problems in statistical mechanics, and string theory. Using the ideas of classical representation theory and basic facts of functional analysis, the author constructs the spin representations of the infinitesimal orthogonal group and the metaplectic representation of an infinite-dimensional symplectic group. A constructive approach is chosen. The author discusses loop algebras and the Virasoro algebra and gives applications in the last chapter. The text addresses graduate students and is of considerable interest to researchers due to a novel approach closer to the traditional line of reasoning in quantum physics.