We compute exactly, in the high-temperature limit, the determ~nant K of small fluctuations around the sphaleron configuration of electroweak theory, exploiting the symmetry of the sphaleron under spatial rotations combined with isospin and custodial SU(2) transformations. For the ratio h / g 2 of scalar four-point coupling ?, to gauge coupling g 2 near unity, we find that K is 0.03. For h / g 2 large corresponding to a strongly coupled Higgs phase, or for h / g 2 very small tending to the Coleman-Weinberg limit, we find that the determinant strongly suppresses the rate of baryonnumber-changing processes.

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The correspondence relations between a fermion field and a boson field in (1+1)-dimensional quantum field theory is discussed in general. Emphases have been laid on the renormalization with respect to an arbitrary mass parameter in boson version as well as the nonlocal property of currents in fermion version. After establishing the equivalence between the continuous chiral transformation in fermion version and the translational transformation in boson version, we are able to prove the Coleman theorem correspondingly.

The fractional fermion number (charge) of (1+1)-dimensional Dirac field interacting with a scalar background field is investigated. By means of the correspondence principle in (1+1)-dimensional field theory, it is shown that only when the background field develops a soliton with a node can the fractional fermion number be induced(node theorem).Consistently, a zero mode bound state of the fermion field should be present and responsible for the fractional charge as long as the soliton satisfies certain conditions (theorem of zero mode).We have also obtained the analytical expression of the vacuum charge distribution in the vicinity of distorted region.