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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Gauge invariant quantization on Riemannian manifolds


Authors: Zhang Ju Liu and Min Qian
Journal: Trans. Amer. Math. Soc. 331 (1992), 321-333
MSC: Primary 58G15; Secondary 58F05, 58F06
DOI: https://doi.org/10.1090/S0002-9947-1992-1040266-0
MathSciNet review: 1040266
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Abstract: For every pointwise polynomial function on each fiber of the cotangent bundle of a Riemannian manifold $ M$, a family of differential operators is given, which acts on the space of smooth sections of a vector bundle on $ M$. Such a correspondence may be considered as a rule to quantize classical systems moving in a Riemannian manifold or in a gauge field. Some applications of our construction are also given in this paper.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1040266-0
Article copyright: © Copyright 1992 American Mathematical Society