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 , a family of differential operators is given, which acts on the space of smooth sections of a vector bundle on . 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1992-1040266-0

Article copyright:
© Copyright 1992
American Mathematical Society