A method of integration over matrix variables. III. (English) Zbl 0745.28006
Summary: For some applications an evaluation of the integral \(Z=\int\exp[-tr V(M)]dM\) over all \(n\times n\) (i) real symmetric, (ii) complex Hermitean, and (iii) quaternion self-dual matrices \(M\) is needed. Here \(V(x)\) is an even polynomial. The case (ii) is known for several years now. We present here a parallel study of the cases (i) and (iii).
[See also Part I in Commun. Math. Phys. 79, 327-340 (1981; Zbl 0471.28007) and Part II in J. Phys. A 14, 579-586 (1981).].
[See also Part I in Commun. Math. Phys. 79, 327-340 (1981; Zbl 0471.28007) and Part II in J. Phys. A 14, 579-586 (1981).].
MSC:
| 28C20 | Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) |
| 46G12 | Measures and integration on abstract linear spaces |
| 81T10 | Model quantum field theories |
