会议论文详细信息
2nd International Symposium on the Modern Physics of Compact Stars and Relativistic Gravity
Kaluza-Klein theory revisited: projective structures and differential operators on algebra of densities
物理学;天文学
Khudaverdian, H.M.^1
School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom^1
关键词: Affine structure;    Differential operators;    Kaluza-Klein theory;    Projective structure;    Scalar product;    Second-order operators;    Subalgebras;   
Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/496/1/012032/pdf
DOI  :  10.1088/1742-6596/496/1/012032
学科分类:天文学(综合)
来源: IOP
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【 摘 要 】

We consider differential operators acting on densities of arbitrary weights on manifold M identifying pencils of such operators with operators on algebra of densities of all weights. This algebra can be identified with the special subalgebra of functions on extended manifold . On one hand there is a canonical lift of projective structures on M to affine structures on extended manifold . On the other hand the restriction of algebra of all functions on extended manifold to this special subalgebra of functions implies the canonical scalar product. This leads in particular to classification of second order operators with use of Kaluza-Klein-like mechanisms.

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