No Access

WHITE NOISE ANALYSIS ON MANIFOLDS AND THE ENERGY REPRESENTATION OF A GAUGE GROUP

TAKAHIRO HASEBE

Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan

https://doi.org/10.1142/S0219025710004243Cited by:0 (Source: Crossref)

Abstract

The energy representation of a gauge group on a Riemannian manifold has been discussed by several authors. Y. Shimada has shown the irreducibility with the use of white noise analysis for compact Riemannian manifolds. In this paper we extend its technique to the noncompact Riemannian manifolds which have differential operators satisfying some conditions.

Keywords:

AMSC: 22E66, 81R10, 60H40

References

S. Albeverio et al. , Noncommutative Distributions. Unitary Representation of Gauge Groups and Algebras ( Marcel Dekker , 1993 ) . Crossref, Google Scholar
S. Albeverio, R. Høegh-Krohn and D. Testard, J. Funct. Anal. 41, 378 (1981), DOI: 10.1016/0022-1236(81)90082-3. Crossref, Web of Science, Google Scholar
I. Chavel , Riemannian Geometry. A Modern Introduction , 2nd edn. ( Cambridge Univ. Press , 2006 ) . Crossref, Google Scholar
I. M. Gelfand, M. I. Graev and A. M. Veršik, Compositio Math. 35, 299 (1977). Web of Science, Google Scholar
I. M. Gelfand, M. I. Graev and A. M. Veršik, Compositio Math. 42, 217 (1981). Web of Science, Google Scholar
T. Hida et al. , White Noise. An Infinite-Dimensional Calculus ( Kluwer , 1993 ) . Google Scholar
R. S. Ismagilov, Unitary representations of the group $C_0 ^{\infty} (M,G)$, $G =$ SU$_2$, Mat. Sb. 100 (1976) 117–131 [English transl. Math. USSR-Sb. 142 (1976) 105–117] . Google Scholar
A. Knapp , Lie Groups Beyond an Introduction , 2nd edn. ( Birkhäuser , 2002 ) . Google Scholar
N. Obata , White Noise Calculus and Fock Space , Lecture Notes in Math 1577 ( Springer-Verlag , 1994 ) . Crossref, Google Scholar
M. Reed and B. Simon , Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis ( Academic Press , 1972 ) . Google Scholar
G. Salomonsen, Res. Math. 39, 115 (2001). Crossref, Google Scholar
Y. Shimada, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 8, 153 (2005), DOI: 10.1142/S0219025705001913. Link, Web of Science, Google Scholar
N. Wallach, Compositio Math. 64, 3 (1987). Web of Science, Google Scholar