Energy in Yang-Mills on a Riemann Surface

Details Energy in Yang-Mills on a Riemann Surface Energy in Yang-Mills on a Riemann Surface

2000-02-10

arxiv.org/abs/math/0002072v1

J.Math.Phys. 41 (2000) 4387-4390

Mathematics

Differential Geometry

7 pages, 2 figures, Latex2e with epsfig, submitted to Journal of Mathematical Physics

Scientific paper

Sengupta's lower bound for the Yang-Mills action on smooth connections on a bundle over a Riemann surface generalizes to the space of connections whose action is finite. In this larger space the inequality can always be saturated. The Yang-Mills critical sets correspond to critical sets of the energy action on a space of paths. This may shed light on Atiyah and Bott's conjecture concerning Morse theory for the space of connections modulo gauge transformations.

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