Duality theorems in BRST cohomology |
| |
Affiliation: | 1. Faculté des Sciences, Université Libre de Bruxelles, Campus Plaine C.P. 231, B-1050 Bruxelles, Belgium;2. Centro de Estudios Cientificos de Santiago, Casilla 16443, Santiago 9, Chile;1. Department of Neuropsychiatry, School of Medicine, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8655, Japan;2. Japan Science and Technology Agency, CREST, 5 Sambancho, Chiyoda-ku, Tokyo 102-0075, Japan |
| |
Abstract: | In classical mechanics, there is no duality theorem relating the BRST cohomologies at positive and negative ghost numbers since these generically fail to be isomorphic. It is shown in this paper, however, that a duality theorem for the BRST operator cohomology can be established in quantum mechanics. Furthermore, when the hermicity properties of the quantum BRST formalism—which are in general just formal—turn out to be actually well defined, this duality theorem also holds for the state cohomology, as a consequence of the non degenerate pairing between subspaces at positive and negative ghost numbers defined by the BRST scalar product. In the case of gauge systems quantized in the Schrödinger representation with compact gauge orbits, the duality theorem contains ordinary Poincaré duality for a compact manifold. In the Fock representation, the duality theorem sheds a new light on existing decoupling theorems. The comparison with the classical situation is also briefly discussed. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|