Monomial integrals on the classical groups

This paper presents a powerful method to integrate general monomials on the classical groups with respect to their invariant (Haar) measure. The method has first been applied to the orthogonal group by one of the authors, Gorin [J. Math. Phys., 43, 3342 (2002)], and is here used to obtain similar in...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of mathematical physics 2008-01, Vol.49 (1), p.013503-013503-20
Hauptverfasser: Gorin, T., López, G. V.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:This paper presents a powerful method to integrate general monomials on the classical groups with respect to their invariant (Haar) measure. The method has first been applied to the orthogonal group by one of the authors, Gorin [J. Math. Phys., 43, 3342 (2002)], and is here used to obtain similar integration formulas for the unitary and the unitary symplectic group. The integration formulas are all recursive, where the recursion parameter is the number of column (row) vectors from which the elements in the monomial are taken. This is an important difference to other integration methods. The integration formulas are easily implemented in a computer algebra environment, which allows us to compute a given monomial integral very efficiently. The result is always a rational function of the matrix dimension.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.2830520