Domain walls at finite temperature

Erratum: Thermal and quantum fluctuations around domain walls [Phys. Rev. D65, 065021 (2002)]

“…Our calculation is just the semiclassical version of that. That estimate has already been made long ago [12], using a different method, as already explained.…”

“…Indeed, for spatial dimension d = 1, our formalism can be adapted to describe fluctuations around defects that occur in one-dimensional systems, such as the solitons found in polymers (like polyacetylene) [10]; and for d = 2, 3, to describe fluctuations around interfaces that separate two distinct phases [11], a description that allows one to calculate how the surface tension, as well as the interface profile are modified by those fluctuations. It can also be used to approximately estimate transition temperatures [12]. Adopting this view, we are able to extract physically relevant results from the study of d > 1, where the action of the domain wall diverges with the size of the system.…”

“…We should point out that expressions for the finite temperature determinant were previously obtained from the explicit knowlegde of the Posch-Teller eigenvalues, either by summing over Matsubara frequencies, and then over those eigenvalues [12], or by integrating over transverse momenta in arbitrary dimension first, making use of dimensional regularization, and then summing over Matsubara frequencies [14].…”

“…The spectrum of the differential operator in (12) is that of a Posch-Teller potential, which is known exactly [17]. Many applications involving kinklike profiles [11][12][13][14]18] have made use of that explicit knowledge of the spectrum. Indeed, in some of them the quadratic propagator was expressed as a sum over the various eigenmodes of the operator, with the respective eigenvalues in the denominator.…”

“…We should point out that a number of works have dealt with similar questions: the finite temperature determinant has been computed long ago [12,14], as a product over eigenvalues; Parnachev and Yaffe [15] have carefully studied the same problem at T = 0, paying special attention to the determinant calculation using a different method. Graham et al [16] have investigated similar problems involving interfaces, resorting to the relation with phase shifts, rather than with the semiclassical propagator.…”