Two-Loop Scalar Kinks

Abstract

At one loop, quantum kinks are described by a sum of quantum harmonic oscillator Hamiltonians, and the ground state is just the product of the oscillator ground states. Two-loop kink masses are only known in integrable and supersymmetric cases and two-loop states have never been found. We find the two-loop kink mass and explicitly construct the two-loop kink ground state in a scalar field theory with an arbitrary nonderivative potential. We use a coherent state operator which maps the vacuum sector to the kink sector, allowing all states to be treated with a single Hamiltonian which needs to be renormalized only once, eliminating the need for regulator matching conditions. Our calculation is greatly simplified by a recently introduced alternative to collective coordinates, in which the kink momentum is fixed perturbatively.

The $ϕ^4$ Kink Mass at Two Loops

“…which in turn was derived in Ref. [8] from the mixing of the free ground state |0 0 = |0 00 0 with a kink state with three virtual normal modes |0 03 1 , given by…”

“…In this note we will be interested in the two-loop correction to the energy of the kink ground state [8]…”

“…(1.3) implies that it will also appear in the kink Hamiltonian density. Our procedure is equivalent to modifying the calculation of [8] by including this counterterm, defined by the condition that the vacuum energy vanishes.…”

Excited Kinks as Quantum States

“…We now review the formalism introduced in Refs. [13,14] that describes quantum kinks in a 1+1d real scalar field theory with Hamiltonian…”

An Alternative to Collective Coordinates

“…The usual IR problems associated to perturbation theory in the presence of a continuous spectrum are resolved here by the momentum constraint (22), as they are resolved in the case of the collective coordinate approach. As this perturbative calculation is standard, it is reported in the companion paper [13]. It yields a general formula valid for the energy of any scalar kink at two loops…”