Abstract
We exploit the 't Hooft–Polyakov monopole to construct closed algebra of the quantum field operators and the BRST charge Q BRST . In the first-class configuration of the Dirac quantization, by including the Q BRST -exact gauge-fixing term and the Faddeev–Popov ghost term, we find the BRST invariant Hamiltonian to investigate the de Rham type cohomology group structure for the monopole system. The Bogomol'nyi bound is also discussed in terms of the first-class topological charge defined on the extended internal two-sphere.
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