Spontaneous symmetry breaking and reflectionless scattering data

Abstract

We consider the question which potentials in the action of a (1+1) dimensional scalar field theory allowing for spontaneous symmetry breaking have quantum fluctuations corresponding to reflectionless scattering data. The general problem of restoration from known scattering data is formulated and a number of explicit examples is given. Only certain sets of reflectionless scattering data correspond to symmetry breaking and all restored potentials are similar either to the Phi**4-model or to the sineGordon model.

From supersymmetric quantum mechanics to scalar field theories

“…The reconstruction of field theory from symmetric reflectionless potentials has already been studied for the case of potentials that support one bound state and two bound states [9,10]. In this section we shall revisit such problem without fixing, at first, the constant c in (16) and verify what happens in both cases.…”

“…We illustrate this with an example, which leads us with two distinct field theories. Reconstruction of field theories from reflectionless symmetric quantum mechanical potentials is an old issue [1][2][3][4][5][6][7][8][9][10]. An interesting fact involving reflectionless potentials is that it can be constructed univocally once the bound state spectrum is known, in a procedure that is sometimes called the spectral method [6,7].…”

Quantum mass correction for the twisted kink

“…These Lamé equations can be understood as fluctuation equations of kink solutions of some quantum field theory on S 1 where the interaction V (φ) is only known implicitly. In the limit R → ∞ the n > 2 Lamé equations will then lead to the reflectionsless potentials considered in [40,34]. with the Riemann zeta function ζ(s).…”

Classical behavior of deformed sine-Gordon models

“…The specific features of these Schrödinger-like problems have been recently explored in Refs. [28,30], to reconstruct the corresponding field theory model. When we write the potential in the form V = W 2 φ /2 we have that…”

“…Among the several possibilities of study, the specific investigations on classical, semiclassical and other aspects of sine-Gordon, double sine-Gordon and related models [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39] have motivated us to propose the present study.…”