Quantum instabilities of solitons

Abstract

We compute the vacuum polarization energies for a couple of soliton models in one space and one time dimensions. These solitons are mappings that connect different degenerate vacua. From the considered sample solitons we conjecture that the vacuum polarization contribution to the total energy leads to instabilities whenever degenerate vacua with different curvatures in field space are accessible to the soliton.

Evidence for the unbinding of the 𝜙4 kink’s shape mode

“…Our method can only be applied to stable kinks, as we require Hamiltonian eigenstates, but using the stability criterion in refs. [25,26] one may easily filter examples. Our formula (3.1) can then be applied to study the evolution of the bound modes.…”

Removing tadpoles in a soliton sector

“…where Q 0 is the mass of the classical kink and M 2 is defined to be V (2) [gf 0 (±∞)]. Note that if f 0 (+∞) = f 0 (−∞) then the quantum kink will accelerate towards the lower energy vacuum and so there is no corresponding Hamiltonian eigenstate and thus no eigenvalue to calculate [9]. Inserting the constant frequency Ansatz φ(x, t) = e −iωt g(x)…”

“…We have assumed that V [gf0(x)] is symmetric about the center of the vortex, a choice which eliminates various classical[8] and quantum[9] instabilities. However the generalization to an arbitrary V [φ] is straightforward.…”

Removing Tadpoles in a Soliton Sector

“…where Q 0 is the mass of the classical kink and M 2 is defined to be V (2) [gf 0 (±∞)]. Note that if f 0 (+∞) = f 0 (−∞) then the quantum kink will accelerate towards the lower energy vacuum and so there is no corresponding Hamiltonian eigenstate and thus no eigenvalue to calculate [8].…”

“…1 We have assumed that V [gf 0 (x)] is symmetric about the center of the vortex, a choice which eliminates various classical [7] and quantum [8] instabilities. However the generalization to an arbitrary V [φ] is straightforward.…”