arXiv subjects

Paul Mansfield

Publications and source records attributed to Paul Mansfield.

39 records · Page 3Linked to original sources

arXiv1995

Topological Renormalisation of the O(3) Sigma Model

We show that the one-instanton sector moduli-space divergence of the O(3) Sigma Model leads to an unacceptable dependence of Green's functions on the arbitrary way that the field is split into a quantum fluctuation about a classical background. Since the divergence is associated with the degeneration of field configurations to those of the zero-instanton sector this arbitrariness may be cancelled by a `topological counter-term' which we construct.

hep-th↗

arXiv1993

Continuum Strong Coupling Expansion of Yang-Mills Theory: Quark Confinement and Infra-Red Slavery

We solve Schrödinger's equation for the ground-state of {\it four}-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading order approximation are reduced to a calculation in {\it two}-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass-scale goes to zero.

hep-th↗

arXiv1993

The Consistency of Topological Expansions in Field Theory: `BRST Anomalies' in Strings and Yang-Mills

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.

hep-th↗