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Dimensional regularisation and instantons

1979; Elsevier BV; Volume: 122; Issue: 2 Linguagem: Inglês

10.1016/0003-4916(79)90206-9

1096-035X

G.M. Shore,

Atomic and Subatomic Physics Research

Abstract Dimensional regularisation is applied to the calculation of the quantum corrections to the instanton tunnelling amplitude in an SU(2) gauge theory. The principal feature is the introduction of an n-dimensional field configuration (a “quasi-instanton”), which generalises the O(5) invariance of the instanton and allows a coordinatisation of the function space of fields in its neighbourhood. This enables the functional integral measure to be factorised, with integrations over the translation and dilatation degrees of freedom being extracted. It is shown that a conformally invariant definition of orthogonality must be used in relation to the zero-mode eigenfunctions of the small oscillations expansion, irrespective of regularisation. An O(n + 1) covariant formalism is employed. An unconventional choice of gauge fixing term, which is not a perfect square, is made and is shown to allow the important freedom of calculating in a gauge specified by an arbitrary parameter α.