Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-08-25
Nucl.Phys. B416 (1994) 205-226
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, DTP-93-45 [original version corrupted by mailer]
Scientific paper
10.1016/0550-3213(94)90583-5
Many field theories of physical interest have configuration spaces consisting of disconnected components. Quantum mechanical amplitudes are then expressed as sums over these components. We use the Faddeev-Popov approach to write the terms in this topological expansion as moduli space integrals. A cut-off is needed when these integrals diverge. This introduces a dependence on the choice of parametrisation of configuration space which must be removed if the theory is to make physical sense. For theories that have a local symmetry this also leads to a breakdown in BRST invariance. We discuss in detail the cases of Bosonic Strings and Yang-Mills theory, showing how this arbitrariness may be removed by the use of a counter-term in the former case, and by compactification on $S\sp 4$ in the latter.
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