arXiv subjects

S. Aubert

Publications and source records attributed to S. Aubert.

2 recordsLinked to original sources

arXiv2004

Invariant and Group Theoretical Integrations over the U(n) Group

In a previous article, an `invariant method' to calculate monomial integrals over the U(n) group was introduced. In this paper, we study the more traditional group-theoretical method, and compare its strengths and weaknesses with those of the invariant method. As a result, we are able to introduce a `hybrid method' which combines the respective strengths of the other two methods. There are many examples in the paper illustrating how each of these methods works.

math-ph↗

arXiv2003

Invariant Integration over the Unitary Group

Integrals for the product of unitary-matrix elements over the U(n) group will be discussed. A group-theoretical formula is available to convert them into a multiple sum, but unfortunately the sums are often tedious to compute. In this paper, we develop an alternative method in which these sums are avoided, and group theory is rendered unnecessary. Only unitarity and the invariance of the Haar measure are required for the computation. The method can also be used to get a closed expression for the simpler integral of monomials over a hypersphere.

math-ph↗