A BRST gauge-fixing procedure for Yang-Mills theory on sphere. (English) Zbl 1247.81503
Summary: A gauge-fixing procedure for the Yang-Mills theory on an \(n\)-dimensional sphere (or a hypersphere) is discussed in a systematic manner. We claim that Adler’s gauge-fixing condition used in massless Euclidean QED on a hypersphere is not conventional because of the presence of an extra free index, and hence is unfavorable for the gauge-fixing procedure based on the BRST invariance principle (or simply BRST gauge-fixing procedure). Choosing a suitable gauge condition, which is proved to be equivalent to a generalization of Adler’s condition, we apply the BRST gauge-fixing procedure to the Yang-Mills theory on a hypersphere to obtain consistent results. Field equations for the Yang-Mills field and associated fields are derived in manifestly \(O(n+1)\) covariant or invariant forms. In the large radius limit, these equations reproduce the corresponding field equations defined on the \(n\)-dimensional flat space.
MSC:
| 81T70 | Quantization in field theory; cohomological methods |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
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